Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

DOI10.1016/j.jde.2018.01.024zbMath1402.35218OpenAlexW2793729614MaRDI QIDQ1701865

Zhifei Zhang, Dong Xiang Chen, Yu-Xi Wang

Publication date: 27 February 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.01.024

zbMATH Keywords

Navier-Stokes equationboundary layerparalinearizationPrandl equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Navier-Stokes equations (35Q30)

Related Items (6)

Global existence and decay estimates of solutions for the compressible Prandtl type equations with small analytic data ⋮ Characteristic boundary layers in the vanishing viscosity limit for the Hunter-Saxton equation ⋮ Separation of the two-dimensional steady MHD boundary layer ⋮ Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow ⋮ Almost global existence for the 3D Prandtl boundary layer equations ⋮ Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space

Cites Work

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• Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation
• Well-posedness for the Prandtl system without analyticity or monotonicity
• Remarks on the ill-posedness of the Prandtl equation
• Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
• Fourier Analysis and Nonlinear Partial Differential Equations
• A note on Prandtl boundary layers
• On the ill-posedness of the Prandtl equation
• Well-Posedness of the Boundary Layer Equations
• On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions
• Well-posedness of the Prandtl equation in Sobolev spaces
• Long time well-posedness of Prandtl system with small and analytic initial data

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