Local solutions to the Navier-Stokes equations with mixed boundary conditions
type: Item
instance of: scholarly article
title: Local solutions to the Navier-Stokes equations with mixed boundary conditions
zbMATH Open document ID: 0924.35097
DOI: 10.1023/A:1006185601807
author: Petr Kučera
author: Zdeněk Skalák
published in: Acta Applicandae Mathematicae
publication date: 1999-11-11T00:00:00Z
review text: The authors prove the existence and uniqueness of solutions of the three-dimensional Navier-Stokes equations and the continuity equation for homogeneous incompressible fluid with mixed boundary conditions. They also formally derive and then give precisely the weak formulation of the Navier-Stokes system. Finally, they prove the existence and uniqueness of solutions of the Navier-Stokes equations on a time interval in general Lipschitz domains and for a wide class of initial conditions. All proofs are based on the method of functional analysis. This is an interesting mathematical work.
reviewed by: Lokenath Debnath
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1267833
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: local solutions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: weak solutions
zbMATH Keywords: Sobolev space with noninteger derivatives
MaRDI profile type: Publication
Recommended article: Local and global solutions of the Navier-Stokes equation
Recommended article: Q3837846
Recommended article: Local in time existence of solution of the Navier-Stokes equations with various types of boundary conditions
Recommended article: Solutions to the Navier-Stokes equations with mixed boundary conditions in two-dimensional bounded domains
Recommended article: On the local solvability of free boundary problem for the Navier-Stokes equations
Recommended article: On local regularity conditions for the Navier–Stokes equations
Recommended article: Nonlocal boundary conditions for the Navier-Stokes equations
Recommended article: The local regularity theory for the Navier-Stokes Equations Near the Boundary
Recommended article: Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions
Recommended article: Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary
description: scientific article; zbMATH DE number 1267833