Almost global existence for the 3D Prandtl boundary layer equations

DOI10.1007/s10440-019-00303-yzbMath1461.76121OpenAlexW2995911725WikidataQ126567387 ScholiaQ126567387MaRDI QIDQ2023052

Ting Zhang, Xueyun Lin

Publication date: 3 May 2021

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-019-00303-y

zbMATH Keywords

Littlewood-Paley theoryalmost global existencePrandtl equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Maximal functions, Littlewood-Paley theory (42B25) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

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Magnetic effects on the solvability of 2D incompressible magneto-micropolar boundary layer equations without resistivity in Sobolev spaces ⋮ Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework ⋮ The well posedness of solutions for the 2D magnetomicropolar boundary layer equations in an analytic framework ⋮ Magneto-micropolar boundary layers theory in Sobolev spaces without monotonicity: well-posedness and convergence theory ⋮ Well-posedness in Gevrey function space for the 3D axially symmetric MHD boundary layer equations without structural assumption ⋮ Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow

Cites Work

• Unnamed Item
• On the ill-posedness of the Prandtl equations in three-dimensional space
• Almost global existence for the Prandtl boundary layer equations
• On the local existence of analytic solutions to the Prandtl boundary layer equations
• The van Dommelen and Shen singularity in the Prandtl equations
• A well-posedness theory for the Prandtl equations in three space variables
• Boundary layers in incompressible Navier-Stokes equations with Navier boundary conditions for the vanishing viscosity limit
• Global regularity for some classes of large solutions to the Navier-Stokes equations
• Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces
• On analytic solutions of the Prandtl equations with Robin boundary condition in half space
• Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I: Existence for Euler and Prandtl equations
• Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II: Construction of the Navier-Stokes solution
• On the global existence of solutions to the Prandtl's system.
• A note on the ill-posedness of shear flow for the MHD boundary layer equations
• Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces
• Local-in-time well-posedness for compressible MHD boundary layer
• Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow
• Boundary layer problem and zero viscosity-diffusion limit of the incompressible magnetohydrodynamic system with no-slip boundary conditions
• Separation for the stationary Prandtl equation
• Formal derivation and stability analysis of boundary layer models in MHD
• Lifespan of solutions to MHD boundary layer equations with analytic perturbation of general shear flow
• Well-posedness for the Prandtl system without analyticity or monotonicity
• Gevrey Class Smoothing Effect for the Prandtl Equation
• Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
• A note on Prandtl boundary layers
• On the ill-posedness of the Prandtl equation
• Blowup of solutions of the unsteady Prandtl's equation
• Well-Posedness of the Boundary Layer Equations
• Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime
• Almost global existence for 2D magnetohydrodynamics boundary layer system
• MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory
• On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions
• Justification of Prandtl Ansatz for MHD Boundary Layer
• Well-posedness of the Prandtl equation in Sobolev spaces
• Long time well-posedness of Prandtl system with small and analytic initial data