Solvability of the Navier-Stokes system with \(L^2\) boundary data
type: Item
instance of: scholarly article
title: Solvability of the Navier-Stokes system with \(L^2\) boundary data
zbMATH Open document ID: 0952.35090
published in: Applied Mathematics and Optimization
publication date: 2001-01-04T00:00:00Z
review text: The author proves the existence of a very weak solution of the Dirichlet problem for the stationary Navier-Stokes system in a bounded domain in \(\mathbb{R}^2\) or in \(\mathbb{R}^3\) with \(L^2\) boundary data. The uniqueness of those solutions is proved under smallness assumptions on the data. First, the penalization method is used to study the linearized problem; then, the Banach fixed point theorem is applied for the nonlinear problem with small boundary data. Results are extended to the case of large data by splitting them into a large regular and small irregular part.
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1462421
zbMATH Keywords: stationary Navier-Stokes equations
zbMATH Keywords: very weak solutions
zbMATH Keywords: nonregular data
zbMATH Keywords: Dirichlet
zbMATH Keywords: uniqueness
zbMATH Keywords: small data
zbMATH Keywords: large data
author: Eduard Marušić-Paloka
MaRDI profile type: Publication
full work available at URL: s002459911018
OpenAlex ID: W2003606678
DOI: 10.1007/S002459911018
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description: scientific article; zbMATH DE number 1462421