Uniqueness theorems for the three dimensional Navier-Stokes system
type: Item
instance of: scholarly article
title: Uniqueness theorems for the three dimensional Navier-Stokes system
zbMATH Open document ID: 0938.35125
DOI: 10.1007/BF02791256
author: Jean-Yves Chemin
published in: Journal d'Analyse Mathématique
publication date: 1999-08-19T00:00:00Z
review text: The author considers the following class of systems of Navier-Stokes type: \[ v_t-\nu\Delta v=Q(v,v) \text{ in }\mathbb{R}^d \times(0,T),\qquad v(0) =v_0\quad \text{ in }\mathbb{R}^d \] for \(d\geq 3\). The operator \(Q\) has the form \[ Q(v,v)= \sum_{j,k}A_{j,k} (D)(v^jv^k), \] where the \(A_{j,k}\) are Fourier multiplication operators that are homogeneous of degree 1. The main results of the paper are existence and uniqueness theorems for functions with values in Besov spaces.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1309899
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Besov spaces
zbMATH Keywords: Cauchy problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
reviewed by: Klaus Deckelnick
MaRDI profile type: Publication
cites work: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: Q4348370
cites work: Q4842676
cites work: Remarques sur l’Existence Globale Pour le Système de Navier–Stokes Incompressible
cites work: Flows of non-Lipschitzian vector fields and Navier-Stokes equations
cites work: Compensated compactness and Hardy spaces
cites work: Q4040820
cites work: On the Navier-Stokes initial value problem. I
cites work: Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces
cites work: Q4376765
cites work: Nonstationary flows of viscous and ideal fluids in \(R^3\)
cites work: Q3684480
cites work: Q4169289
cites work: Q4629102
description: scientific article; zbMATH DE number 1309899