On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
From MaRDI portal
Publication:5459236
DOI10.1515/CRELLE.2008.013zbMath1145.35053MaRDI QIDQ5459236
Yoshihiro Shibata, Senjo Shimizu
Publication date: 25 April 2008
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Smoothness and regularity of solutions to PDEs (35B65) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)
Related Items (53)
Maximal \(L^p-L^q\) regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation ⋮ Maximal \(L^1\)-regularity for parabolic initial-boundary value problems with inhomogeneous data ⋮ Global well posedness for a Q-tensor model of nematic liquid crystals ⋮ Reacting multi-component fluids: regular solutions in Lorentz spaces ⋮ Maximal regularity for compressible two-fluid system ⋮ On the free boundary problem for the Oldroyd-B model in the maximal \(L_p-L_q\) regularity class ⋮ On a fluid–structure interaction problem for plaque growth ⋮ On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain ⋮ Maximal regularity for the thermoelastic plate equations with free boundary conditions ⋮ On the global well-posedness of strong dynamics of incompressible nematic liquid crystals in \(\mathbb R^N\) ⋮ Global solvability in a two-dimensional self-consistent chemotaxis-Navier-Stokes system ⋮ Global solvability of the Navier-Stokes equations with a free surface in the maximal \(L_{p}-L_{q}\) regularity class ⋮ On the Stokes system in cylindrical domains ⋮ Global well-posedness of the Navier-Stokes equations in homogeneous Besov spaces on the half-space ⋮ The \(\mathcal{R}\)-bounded operator families arising from the study of the barotropic compressible flows with free surface ⋮ Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension ⋮ On the Neumann problem for the nonstationary Stokes system in angles and cones ⋮ Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation ⋮ On the global wellposedness of free boundary problem for the Navier-Stokes system with surface tension ⋮ One Navier's problem for the Brinkman system ⋮ Generalized resolvent estimates of the Stokes equations with first order boundary condition in a general domain ⋮ On the maximal \(L_{p}\)-\(L_{q}\) regularity of the Stokes problem with first order boundary condition; model problems ⋮ Asymptotic dynamics on a chemotaxis-Navier–Stokes system with nonlinear diffusion and inhomogeneous boundary conditions ⋮ Global well-posedness for the incompressible Navier-Stokes equations in the critical Besov space under the Lagrangian coordinates ⋮ Convergence of the Neumann series in BEM for the Neumann problem of the Stokes system ⋮ On some free boundary problem for a compressible barotropic viscous fluid flow ⋮ On a maximal \(L_p - L_q\) approach to the compressible viscous fluid flow with slip boundary condition ⋮ The Neumann problem for the planar Stokes system ⋮ The Global Well-Posedness for the Compressible Fluid Model of Korteweg Type ⋮ ℛ $${\mathcal R}$$ Boundedness, Maximal Regularity and Free Boundary Problems for the Navier Stokes Equations ⋮ Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows ⋮ Strong solutions to compressible-incompressible two-phase flows with phase transitions ⋮ Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions ⋮ Sharp interface limit of a Stokes/Cahn-Hilliard system. I: Convergence result ⋮ Maximal \(L_{p}-L_{q}\) regularity of the linearized initial-boundary value problem for motion of compressible viscous fluids ⋮ Maximal \(L_{p}\)-\(L_{q}\) regularity for the two-phase Stokes equations; model problems ⋮ Global existence and boundedness for chemotaxis-Navier-Stokes systems with position-dependent sensitivity in 2D bounded domains ⋮ Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system ⋮ On the isothermal compressible multi-component mixture flow: the local existence and maximal \(L_p-L_q\) regularity of solutions ⋮ Integral representation of a solution of the Neumann problem for the Stokes system ⋮ On the maximal \(L_{p}-L_{q}\) regularity of solutions to a general linear parabolic system ⋮ On the maximal \(L_p-L_q\) regularity for a compressible fluid model of Korteweg type on general domains ⋮ The Work of Yoshihiro Shibata ⋮ Report on a local in time solvability of free surface problems for the Navier–Stokes equations with surface tension ⋮ Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains ⋮ Maximal \(L^1\)-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space ⋮ Resolvent estimates for a compressible fluid model of Korteweg type and their application ⋮ The time periodic problem of the Navier-Stokes equations in a bounded domain with moving boundary ⋮ On Strong Dynamics of Compressible Two-Component Mixture Flow ⋮ On the \(L_{p}\) analytic semigroup associated with the linear thermoelastic plate equations in the half-space ⋮ On some free boundary problem of the Navier-Stokes equations in the maximal \(L_p - L_q\) regularity class ⋮ About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain ⋮ On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface
Cites Work
- On the Oseen equation in the three dimensional exterior domains
- Optimal \(L^{p}\)- \(L^{q}\)-estimates for parabolic boundary value problems with inhomogeneous data
- Pseudo-differential boundary problems in Lp, spaces
- CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
- ON THE TRANSIENT MOTION OF AN ISOLATED VOLUME OF VISCOUS INCOMPRESSIBLE FLUID
- Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
This page was built for publication: On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
