Remarks on the ill-posedness of the Prandtl equation
From MaRDI portal
Publication:2883249
zbMath1238.35178arXiv1008.0532MaRDI QIDQ2883249
David Gérard-Varet, Toan T. Nguyen
Publication date: 11 May 2012
Full work available at URL: https://arxiv.org/abs/1008.0532
Related Items
Almost global existence for the Prandtl boundary layer equations ⋮ Gevrey stability of Prandtl expansions for 2-dimensional Navier-Stokes flows ⋮ Steady Prandtl layer expansions with external forcing ⋮ On back flow of boundary layers in two-dimensional unsteady incompressible heat conducting flow ⋮ Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay ⋮ A note on the ill-posedness of shear flow for the MHD boundary layer equations ⋮ On the Euler\(+\)Prandtl expansion for the Navier-Stokes equations ⋮ The vanishing viscosity limit in the presence of a porous medium ⋮ Ill-posedness of the hydrostatic Euler and singular Vlasov equations ⋮ Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime ⋮ Boundary layer problems for the two-dimensional compressible Navier–Stokes equations ⋮ On the Ill-Posedness of the Triple Deck Model ⋮ On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: Illposedness near degenerate stationary solutions ⋮ Regularized Euler-\(\alpha \) motion of an infinite array of vortex sheets ⋮ Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate ⋮ Sublayer of Prandtl boundary layers ⋮ Global small analytic solutions of MHD boundary layer equations ⋮ Magnetic effects on the solvability of 2D incompressible magneto-micropolar boundary layer equations without resistivity in Sobolev spaces ⋮ Formal derivation and stability analysis of boundary layer models in MHD ⋮ Regularity and expansion for steady Prandtl equations ⋮ Long time well-posedness of Prandtl equations in Sobolev space ⋮ The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary ⋮ On the well-posedness of reduced \(3D\) primitive geostrophic adjustment model with weak dissipation ⋮ Dynamic stability for steady Prandtl solutions ⋮ Lifespan of solutions to MHD boundary layer equations with analytic perturbation of general shear flow ⋮ On the Prandtl boundary layer equations in presence of corner singularities ⋮ Viscous-inviscid interactions in a boundary-layer flow induced by a vortex array ⋮ Long‐Time Instability of the Couette Flow in Low Gevrey Spaces ⋮ Validity of steady Prandtl layer expansions ⋮ On the role of the displacement current and the Cattaneo's law on boundary layers of plasma ⋮ Improved well-posedness for the triple-deck and related models via concavity ⋮ Boundary Vorticity Estimates for Navier–Stokes and Application to the Inviscid Limit ⋮ Global existence and decay estimates of solutions for the compressible Prandtl type equations with small analytic data ⋮ On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class ⋮ Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations ⋮ On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows ⋮ Magneto-micropolar boundary layers theory in Sobolev spaces without monotonicity: well-posedness and convergence theory ⋮ On the steady Prandtl boundary layer expansions ⋮ Higher regularity and asymptotic behavior of 2D magnetic Prandtl model in the Prandtl-Hartmann regime ⋮ Well-posedness in Gevrey function space for the 3D axially symmetric MHD boundary layer equations without structural assumption ⋮ On the hydrostatic Navier-Stokes equations with Gevrey class 2 data ⋮ Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces ⋮ The Three-Dimensional Inviscid Limit Problem with Data Analytic Near the Boundary ⋮ Local well-posedness of solutions to the boundary layer equations for 2D compressible flow ⋮ Local-in-time well-posedness for compressible MHD boundary layer ⋮ On a global weak solution and back flow of the mixed Prandtl-Hartmann boundary layer problem ⋮ The inviscid limit of Navier-Stokes equations for analytic data on the half-space ⋮ Remarks on the Prandtl boundary layer ⋮ The van Dommelen and Shen singularity in the Prandtl equations ⋮ A well-posedness theory for the Prandtl equations in three space variables ⋮ Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow ⋮ Steady Prandtl boundary layer expansions over a rotating disk ⋮ Zero-viscosity limit of the Navier-Stokes equations in the analytic setting ⋮ Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation ⋮ Local well-posedness for linearized degenerate MHD boundary layer equations in analytic setting ⋮ Well-posedness of the Prandtl equations without any structural assumption ⋮ Global steady Prandtl expansion over a moving boundary. I ⋮ Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain ⋮ The vanishing viscosity limit for 2D Navier-Stokes in a rough domain ⋮ Global existence and the decay of solutions to the Prandtl system with small analytic data ⋮ Long time well-posedness of Prandtl system with small and analytic initial data ⋮ A blow-up criterion for classical solutions to the Prandtl equations ⋮ Zero-viscosity limit of the Navier-Stokes equations in a simply-connected bounded domain under the analytic setting ⋮ Gevrey Class Smoothing Effect for the Prandtl Equation ⋮ Back Flow of the Two-dimensional Unsteady Prandtl Boundary Layer Under an Adverse Pressure Gradient ⋮ On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion ⋮ Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow ⋮ \(L^\infty\) instability of Prandtl layers ⋮ Justification of Prandtl Ansatz for MHD Boundary Layer ⋮ Well-posedness issues for the Prandtl boundary layer equations ⋮ The vanishing viscosity limit for some symmetric flows ⋮ Boundary Layer Expansions for the Stationary Navier-Stokes Equations ⋮ On the inviscid limit of the Navier-Stokes equations ⋮ Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces ⋮ Well-posedness of the Prandtl equation in Sobolev spaces ⋮ Remarks on the Inviscid Limit for the Navier--Stokes Equations for Uniformly Bounded Velocity Fields ⋮ On the ill-posedness of the Prandtl equations in three-dimensional space
