Remarks on vanishing viscosity limits for the 3D Navier-Stokes equations with a slip boundary condition

DOI10.1007/s11401-011-0649-0zbMath1305.35106OpenAlexW2093759429MaRDI QIDQ741420

Yuelong Xiao, Zhouping Xin

Publication date: 12 September 2014

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-011-0649-0

zbMATH Keywords

Poincaré inequalitySobolev spaces with variable exponent

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Navier-Stokes equations for incompressible viscous fluids (76D05) Singular perturbations in context of PDEs (35B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Navier-Stokes equations (35Q30) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10) Applications of functional analysis to differential and integral equations (46N20) Viscosity solutions to PDEs (35D40)

Related Items (15)

On 3D Lagrangian Navier-Stokes \(\alpha\) model with a class of vorticity-slip boundary conditions ⋮ Weak solutions to the two-dimensional steady compressible Navier-Stokes equations ⋮ Small-time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions ⋮ Vanishing viscous limits for 3D Navier-Stokes equations with a Navier-slip boundary condition ⋮ Vanishing diffusivity limit for the 3D heat-conductive Boussinesq equations with a slip boundary condition ⋮ A survey on some vanishing viscosity limit results ⋮ Vanishing viscosity limits for the 3D Navier-Stokes equations with a slip boundary condition ⋮ Boundary layer for a class of nonlinear pipe flow ⋮ An elementary approach to the inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations ⋮ On the inviscid limit of the 3D Navier-Stokes equations with generalized Navier-slip boundary conditions ⋮ On the vanishing viscosity limit of 3D Navier-Stokes equations under slip boundary conditions in general domains ⋮ On the vanishing dissipation limit for the incompressible MHD equations on bounded domains ⋮ A note on the Euler-Voigt system in a 3D bounded domain: propagation of singularities and absence of the boundary layer ⋮ On the Boussinesq system: local well-posedness of the strong solution and inviscid limits ⋮ A new boundary condition for the three-dimensional Navier-Stokes equation and the vanishing viscosity limit

Cites Work

• Nonlinear evolution equations and the Euler flow
• On a \(\nu\)-continuous family of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition
• Infinite-dimensional dynamical systems in mechanics and physics.
• Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case
• Remarks on the Euler equation
• Sharp inviscid limit results under Navier-type boundary conditions. An \(L^p\) theory
• On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition
• Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions

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