\(L^p\)-theory for Stokes and Navier-Stokes equations with Navier boundary condition

DOI10.1016/j.jde.2013.11.005zbMath1285.35063OpenAlexW2078650615MaRDI QIDQ2438817

Ahmed Rejaiba, Chérif Amrouche

Publication date: 6 March 2014

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

Full work available at URL: https://doi.org/10.1016/j.jde.2013.11.005

zbMATH Keywords

Navier-Stokes equationsStokes equationsfluid mechanicsvery weak solutions\(L^p\)-theoryNavier boundary conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• Unnamed Item
• Stationary Stokes, Oseen and Navier-Stokes equations with singular data
• On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
• Mixed finite element approximation of the vector potential
• On a boundary value problem for a stationary system of Navier-Stokes equations
• On incompressible viscous fluid flows with slip boundary conditions.
• Why viscous fluids adhere to rugose walls: A mathematical explanation.
• Sharp inviscid limit results under Navier-type boundary conditions. An \(L^p\) theory
• On the Stokes equations with the Navier-type boundary conditions
• On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
• Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
• L^p-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS