The initial value problem for the Navier-Stokes equations with general slip boundary condition in Hölder spaces
type: Item
instance of: scholarly article
title: The initial value problem for the Navier-Stokes equations with general slip boundary condition in Hölder spaces
zbMATH Open document ID: 1048.35057
author: Atusi Tani
author: Shigeharu Itoh
author: Naoto Tanaka
published in: Journal of Mathematical Fluid Mechanics
publication date: 2003-08-27T00:00:00Z
review text: The authors study the initial-boundary value problem for incompressible Navier-Stokes equations with general slip boundary condition on a solid boundary. The unique solvability is established in anisotropic Hölder spaces locally in time for three-dimensional problem, and globally in time for two-dimensional problem without smallness restrictions. The authors approximate the solutions of Navier-Stokes systems by solutions of a linearized homogeneous Stokes-type system, and then prove the convergence of successive approximations.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 1971869
zbMATH Keywords: unique solvability
zbMATH Keywords: linearized homogeneous Stokes-type system
zbMATH Keywords: convergence of successive approximations
zbMATH Keywords: anisotropic Hölder spaces
MaRDI profile type: Publication
full work available at URL: s00021-003-0074-6
OpenAlex ID: W1642056360
DOI: 10.1007/S00021-003-0074-6
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description: scientific article; zbMATH DE number 1971869