Verification of Prandtl Boundary Layer Ansatz for Steady Electrically Conducting Fluids with a Moving Physical Boundary

DOI10.1137/20M1317736zbMath1473.76075arXiv2001.00324MaRDI QIDQ3383040

Shijin Ding, Feng Xie, Zhilin Lin

Publication date: 23 September 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00324

zbMATH Keywords

Sobolev spaceerror estimatehigh Reynolds number limitincompressible boundary layer expansion

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items

Validity of Prandtl layer expansions for steady magnetohydrodynamics over a rotating disk ⋮ Validity of Prandtl Expansions for Steady MHD in the Sobolev Framework

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Steady Prandtl boundary layer expansions over a rotating disk
• Zero-viscosity limit of the Navier-Stokes equations in the analytic setting
• 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
• Gevrey stability of Prandtl expansions for 2-dimensional Navier-Stokes flows
• Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate
• Global steady Prandtl expansion over a moving boundary. I
• Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain
• Global steady Prandtl expansion over a moving boundary. II
• Global steady Prandtl expansion over a moving boundary. III
• 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
• Sobolev stability of Prandtl expansions for the steady Navier-Stokes equations
• Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
• On the steady Prandtl type equations with magnetic effects arising from 2D incompressible MHD equations in a half plane
• MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory
• Justification of Prandtl Ansatz for MHD Boundary Layer
• Well-posedness of the Prandtl equation in Sobolev spaces
• On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane