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Almost Global Existence for the Prandtl Boundary Layer Equations

https://doi.org/10.1007/s00205-015-0942-2
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Blowup of solutions of the unsteady Prandtl's equation
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On the nonlinear instability of Euler and Prandtl equations
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Existence and Singularities for the Prandtl Boundary Layer Equations
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A note on Prandtl boundary layers
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On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane
inferredcites →https://doi.org/10.1002/cpa.21595openalex-snapshot
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
inferredcites →https://doi.org/10.1002/cpa.3160360304openalex-snapshot
On “almost global” solutions to quasilinear wave equations in three space dimensions
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On the Stability of Boundary Layers of Incompressible Euler Equations
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On the Domain of Analyticity for Solutions of Second Order Analytic Nonlinear Differential Equations
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The Analysis of Linear Partial Differential Operators III
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The analysis of linear partial differential operators
inferredcites →https://doi.org/10.1007/s00021-010-0032-zopenalex-snapshot
Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations
inferredcites →https://doi.org/10.1007/s00205-011-0485-0openalex-snapshot
On the H s Theory of Hydrostatic Euler Equations
inferredcites →https://doi.org/10.1007/s002200050304openalex-snapshot
Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations
inferredcites →https://doi.org/10.1007/s40818-016-0020-6openalex-snapshot
Prandtl Boundary Layer Expansions of Steady Navier–Stokes Flows Over a Moving Plate
inferredcites →https://doi.org/10.1016/0021-8928(66)90001-3openalex-snapshot
On the mathematical theory of boundary layer for an unsteady flow of incompressible fluid
inferredcites →https://doi.org/10.1016/j.aim.2016.12.025openalex-snapshot
A well-posedness theory for the Prandtl equations in three space variables
inferredcites →https://doi.org/10.1016/j.jde.2010.07.032openalex-snapshot
Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain
inferredcites →https://doi.org/10.1016/j.physd.2009.07.007openalex-snapshot
Singularity formation for Prandtl’s equations
inferredcites →https://doi.org/10.1016/s0001-8708(03)00046-xopenalex-snapshot
On the global existence of solutions to the Prandtl's system
inferredcites →https://doi.org/10.1016/s0764-4442(00)01798-5openalex-snapshot
Existence and uniqueness for the Prandtl equations
inferredcites →https://doi.org/10.1017/cbo9780511616938openalex-snapshot
Hydrodynamic Stability
inferredcites →https://doi.org/10.1017/s1474748013000212openalex-snapshot
Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data
inferredcites →https://doi.org/10.1063/1.4753991openalex-snapshot
Local existence of solutions to the free boundary value problem for the primitive equations of the ocean
inferredcites →https://doi.org/10.1090/s0002-9939-2015-12638-xopenalex-snapshot
On the inviscid limit of the Navier-Stokes equations
inferredcites →https://doi.org/10.1090/s0894-0347-09-00652-3openalex-snapshot
On the ill-posedness of the Prandtl equation
inferredcites →https://doi.org/10.1090/s0894-0347-2014-00813-4openalex-snapshot
Well-posedness of the Prandtl equation in Sobolev spaces
inferredcites →https://doi.org/10.1115/1.3162197openalex-snapshot
Hydrodynamic Stability
inferredcites →https://doi.org/10.1137/140956440openalex-snapshot
On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions
inferredcites →https://doi.org/10.1137/140978466openalex-snapshot
Local Well-Posedness of Prandtl Equations for Compressible Flow in Two Space Variables
inferredcites →https://doi.org/10.1137/s0036141002412057openalex-snapshot
Well-Posedness of the Boundary Layer Equations
inferredcites →https://doi.org/10.1515/anly-2015-0001openalex-snapshot
Spectral stability of Prandtl boundary layers: An overview
inferredcites →https://doi.org/10.24033/asens.2270openalex-snapshot
Well-posedness for the Prandtl system without analyticity or monotonicity
inferredcites →https://doi.org/10.3233/asy-2011-1075openalex-snapshot
Remarks on the ill-posedness of the Prandtl equation
inferredcites →https://doi.org/10.3934/dcds.2011.29.285openalex-snapshot
The domain of analyticity of solutions to the three-dimensional Euler equations in a half space
inferredcites →https://doi.org/10.4007/annals.2011.173.2.9openalex-snapshot
Global regularity for some classes of large solutions to the Navier-Stokes equations
inferredcites →https://doi.org/10.4310/cms.2003.v1.n2.a5openalex-snapshot
Singularity Formation and Instability in the Unsteady Inviscid and Viscous Prandtl Equations
inferredcites →https://doi.org/10.4310/cms.2013.v11.n1.a8openalex-snapshot
On the local existence of analytic solutions to the Prandtl boundary layer equations
inferredcites →https://doi.org/10.48550/arxiv.1402.1395openalex-snapshot
Spectral instability of symmetric shear flows in a two-dimensional channel
inferredcites →https://doi.org/10.48550/arxiv.1403.5748openalex-snapshot
On the inviscid limit of the Navier-Stokes equations
inferredcites →https://doi.org/10.48550/arxiv.1409.1648openalex-snapshot
Long time well-posdness of Prandtl system with small and analytic initial data
inferredcites →https://doi.org/10.5802/slsedp.82openalex-snapshot
On the spectral instability of parallel shear flows

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Global Small Solutions of Mhd Boundary Layer Equations in Gevrey Function Space
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The Growth Mechanism of Boundary Layers for the 2d Navier-Stokes Equations
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The Growth Mechanism of Boundary Layers for the 2d Navier-Stokes Equations
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MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory
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Real Analytic Local Well‐Posedness for the Triple Deck
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Validity of steady Prandtl layer expansions
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Global‐in‐time well‐posedness of solutions for the 2D hyperbolic Prandtl equations in an analytic framework
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Local Well‐Posedness to the Magneto‐Micropolar Boundary Layer Equations in Gevrey Space
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Almost global existence for 2D magnetohydrodynamics boundary layer system
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Well‐posedness of thermal boundary layer equation in two‐dimensional incompressible heat conducting flow with analytic datum
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Long time well‐posedness of two dimensional Magnetohydrodynamic boundary layer equation without resistivity
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The Inviscid Limit and Boundary Layers for Navier-Stokes Flows
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The Inviscid Limit and Boundary Layers for Navier-Stokes Flows
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Survey on the Prandtl Equations and Related Boundary Layer Equations
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Global Well-Posedness of Solutions to the 2D Prandtl-Hartmann Equations in an Analytic Framework
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Local Well-Posedness of Solutions to the 2D Mixed Prandtl Equations in a Sobolev Space Without Monotonicity and Lower Bound
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Well-posedness and Blowup of the Geophysical Boundary Layer Problem
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On the Euler$$+$$Prandtl Expansion for the Navier-Stokes Equations
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Improved Well-Posedness for the Triple-Deck and Related Models via Concavity
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Well-Posedness in Gevrey Function Space for the 3D Axially Symmetric MHD Boundary Layer Equations Without Structural Assumption
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Bv entropy solutions of two-dimensional nonstationary Prandtl boundary layer system
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Steady Prandtl Boundary Layer Expansions Over a Rotating Disk
inferred← citeshttps://doi.org/10.1007/s00205-018-1235-3openalex-snapshot
Sublayer of Prandtl Boundary Layers
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The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space
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The Inviscid Limit for the Navier–Stokes Equations with Data Analytic Only Near the Boundary
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Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data
inferred← citeshttps://doi.org/10.1007/s00220-021-03964-9openalex-snapshot
Regularity and Expansion for Steady Prandtl Equations
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Landau Damping, Collisionless Limit, and Stability Threshold for the Vlasov-Poisson Equation with Nonlinear Fokker-Planck Collisions
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Local-in-Time Well-Posedness for 2D Compressible Magneto-micropolar Boundary Layer Equations in Sobolev Spaces
inferred← citeshttps://doi.org/10.1007/s00332-024-10032-8openalex-snapshot
Nonuniqueness of Generalised Weak Solutions to the Primitive and Prandtl Equations
inferred← citeshttps://doi.org/10.1007/s00526-021-01958-yopenalex-snapshot
Boundary layer problems for the two-dimensional inhomogeneous incompressible magnetohydrodynamics equations
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Magneto-micropolar boundary layers theory in Sobolev spaces without monotonicity: well-posedness and convergence theory
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On the hydrostatic Navier–Stokes equations with Gevrey class 2 data
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Local Well-posedness for Linearized Degenerate MHD Boundary Layer Equations in Analytic Setting
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Local Well-posedness of 2D Two-Phase Compressible MHD Boundary Layer Equations Without Resistivity
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Lifespan of Solutions to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow
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Almost Global Existence for the 3D Prandtl Boundary Layer Equations
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Global well-posedness of a Prandtl model from MHD in Gevrey function spaces
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Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations
inferred← citeshttps://doi.org/10.1007/s11425-025-2456-6openalex-snapshot
Global well-posedness of the MHD boundary layer equations in the Sobolev space
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Gevrey well-posedness of the MHD-wave boundary layer equations without any structure assumption
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Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space
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Regularized Euler- $$\alpha $$ α motion of an infinite array of vortex sheets
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Controllability of the Navier–Stokes Equation in a Rectangle with a Little Help of a Distributed Phantom Force
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Dynamic Stability for Steady Prandtl Solutions
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Global Steady Prandtl Expansion over a Moving Boundary I
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Global Steady Prandtl Expansion over a Moving Boundary II
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The van Dommelen and Shen singularity in the Prandtl equations
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A well-posedness theory for the Prandtl equations in three space variables
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On the hydrostatic approximation of the Navier-Stokes equations in a thin strip
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On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class
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Blow-up of solutions of the hyperbolic Prandtl system
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Long time well-posedness of Prandtl equations in Sobolev space
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Local-in-time well-posedness for compressible MHD boundary layer
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Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain
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Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile
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Global small analytic solutions of MHD boundary layer equations
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Global solvability of 2D MHD boundary layer equations in analytic function spaces
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Global small solutions of MHD boundary layer equations in Gevrey function space*
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Higher regularity and asymptotic behavior of 2D magnetic Prandtl model in the Prandtl-Hartmann regime
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The growth mechanism of boundary layers for the 2D Navier-Stokes equations
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The local well-posedness of analytic solution to the boundary layer system for compressible flow in three dimensions
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A well-posedness theory for the MHD boundary layer equations in three space variables
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Vanishing diffusivity limit for the Boussinesq equations with Dirichlet boundary conditions
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Local well-posedness in Gevrey function spaces for 3D Boussinesq boundary layer system
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Well-posedness of the compressible boundary layer equations with analytic initial data
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Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
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Global existence and decay estimates of solutions for the compressible Prandtl type equations with small analytic data
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On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows
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Gevrey Well-posedness of the MHD boundary layer system with temperature
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Global well-posedness of 2D Hyperbolic perturbation of the Navier–Stokes system in a thin strip
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Local well-posedness of solutions to 2D mixed Prandtl equations in Sobolev space without monotonicity and lower bound
inferred← citeshttps://doi.org/10.1016/j.nonrwa.2025.104448openalex-snapshot
Sobolev stability of hydrostatic ideal MHD equations in a thin domain
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Global inviscid limit of 2D, stationary Navier-Stokes and stability of Prandtl expansions
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Local well-posedness for 2D incompressible magneto-micropolar boundary layer system
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Steady Prandtl layer expansions with external forcing
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Remark on the ill-posedness of the hyperbolic Prandtl system
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Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime
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Justification of Prandtl Ansatz for MHD Boundary Layer
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Back Flow of the Two-dimensional Unsteady Prandtl Boundary Layer Under an Adverse Pressure Gradient
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The Three-Dimensional Inviscid Limit Problem with Data Analytic Near the Boundary
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Well-posedness of the MHD Boundary Layer System in Gevrey Function Space without Structural Assumption
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On the Hydrostatic Approximation of the MHD Equations in a Thin Strip
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On the Hydrostatic Approximation of the 3D Boussinesq Equations of Damped Wave Type
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Global Gevrey-2 solutions of the 3D axially symmetric Prandtl equations
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Global well-posedness of the 3D axially symmetric magnetohydrodynamic boundary layer equations in an analytic space
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The well posedness of solutions for the 2D magnetomicropolar boundary layer equations in an analytic framework
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Global well-posedness and finite time blowup of the Prandtl equation
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Mathematical analysis of boundary layers in two-dimensional incompressible viscous heat conducting flows
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Paralinearization method about the well-posedness of the Prandtl equation
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Global stability of monotone shear flows for the 2-D Prandtl system in Sobolev spaces
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The local well-posedness of the three-dimensional compressible isentropic boundary layer equations
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Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
inferred← citeshttps://doi.org/10.2140/apde.2020.13.1417openalex-snapshot
Well-posedness of the hydrostatic Navier–Stokes equations
inferred← citeshttps://doi.org/10.3233/asy-191593openalex-snapshot
Global well-posedness of the 2-D magnetic Prandtl model in the Prandtl–Hartmann regime
inferred← citeshttps://doi.org/10.3934/cpaa.2026042openalex-snapshot
Gevrey well-posedness of the hydrostatic MHD-wave system
inferred← citeshttps://doi.org/10.3934/dcds.2023133openalex-snapshot
Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces
inferred← citeshttps://doi.org/10.3934/dcdss.2024189openalex-snapshot
Global existence and uniqueness of solutions to the Prandtl-Hartmann boundary layer equations
inferred← citeshttps://doi.org/10.3934/dcdss.2025130openalex-snapshot
Long time well-posedness of solutions for the 2D magneto-micropolar boundary layer equations in Sobolev framework
inferred← citeshttps://doi.org/10.3934/dcdss.2026148openalex-snapshot
Lifespan of solutions for the 2D MHD-wave boundary layer equation in an analytic framework
inferred← citeshttps://doi.org/10.3934/dcdss.2026193openalex-snapshot
The local well-posedness of analytic solutions to the 3D Boussinesq boundary layer equations
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Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity
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Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space
inferred← citeshttps://doi.org/10.3934/era.2026068openalex-snapshot
Well-posedness of the 3D MHD boundary layer equations in an analytic space
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Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space
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3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space
inferred← citeshttps://doi.org/10.4208/cmaa.2023-0007openalex-snapshot
Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations
inferred← citeshttps://doi.org/10.4208/cmaa.2024-0020openalex-snapshot
Local Well-Posedness of the Three Dimensional Linearized MHD Boundary Layer System
inferred← citeshttps://doi.org/10.4208/cmaa.2026-0001openalex-snapshot
Analyticity up to the Boundary for the 2D and 3D Prandtl Equations
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On Well-Posedness of the Boundary Layer Problem Without the Monotonicity Assumption in the Compressible Non-Isentropic Flow
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Gevrey Well-Posedness of the Hyperbolic Prandtl Equations
inferred← citeshttps://doi.org/10.4208/jpde.v35.n3.7openalex-snapshot
Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework
inferred← citeshttps://doi.org/10.48550/arxiv.1511.04850openalex-snapshot
Long time well-posdness of the Prandtl equations in Sobolev space
inferred← citeshttps://doi.org/10.48550/arxiv.1609.08430openalex-snapshot
Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical points
inferred← citeshttps://doi.org/10.48550/arxiv.1704.06766openalex-snapshot
Local-in-time Well-posedness of Boundary Layer System for the Full Incompressible MHD Equations by Energy Methods
inferred← citeshttps://doi.org/10.48550/arxiv.1708.08217openalex-snapshot
Well-posedness in Gevrey function space for the three-dimensional Prandtl equations
inferred← citeshttps://doi.org/10.48550/arxiv.1801.01860openalex-snapshot
Controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force
inferred← citeshttps://doi.org/10.48550/arxiv.1801.10481openalex-snapshot
Separation of the two-dimensional unsteady Prandtl boundary layers under an adverse pressure gradient
inferred← citeshttps://doi.org/10.48550/arxiv.1803.06681openalex-snapshot
Local-in-time well-posedness for Compressible MHD boundary layer
inferred← citeshttps://doi.org/10.48550/arxiv.1811.11412openalex-snapshot
Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain
inferred← citeshttps://doi.org/10.48550/arxiv.1905.07640openalex-snapshot
Real analytic local well-posedness for the Triple Deck
inferred← citeshttps://doi.org/10.48550/arxiv.1910.14449openalex-snapshot
The 3D inviscid limit problem with data analytic near the boundary
inferred← citeshttps://doi.org/10.48550/arxiv.1911.03690openalex-snapshot
Global existence and decay of solutions to Prandtl system with small analytic data
inferred← citeshttps://doi.org/10.48550/arxiv.2002.06327openalex-snapshot
Blow-up criterion for the 2-D Prandtl equation
inferred← citeshttps://doi.org/10.48550/arxiv.2008.12347openalex-snapshot
Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
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