\(L_p\)-\(L_q\) maximal regularity and viscous incompressible flows with free surface

DOI10.3792/pjaa.81.151zbMath1188.35139OpenAlexW2094400159MaRDI QIDQ935671

Senjo Shimizu, Yoshihiro Shibata

Publication date: 12 August 2008

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.81.151

zbMATH Keywords

Navier-Stokes equationsfree boundary problemNeumann boundary conditionStokes equationsmaximal regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35)

Related Items

The time-dependent Stokes problem with Navier slip boundary conditions on \(L^p\)-spaces, Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids, On varifold solutions of two-phase incompressible viscous flow with surface tension, A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space, The Work of Yoshihiro Shibata, Maximal \(L^1\)-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space, Discrete maximal regularity for abstract Cauchy problems

Cites Work

• On a resolvent estimate for the Stokes system with Neumann boundary condition.
• Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods.
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity