On some modification Navier-Stokes equations
type: Item
instance of: scholarly article
title: On some modification Navier-Stokes equations
zbMATH Open document ID: 1041.35055
DOI: 10.1016/S0362-546X(02)00132-3
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The author considers the modified Navier-Stokes system, proposed by \textit{J.-L. Lions} [Quelques méthodes de résolution des problèmes aux limites non linéares. Paris: Dunod (1969; Zbl 0189.40603)]: \[ \partial_t u_j- \mu \sum^n_{i=1} \partial_i(| u_j|^{p_i-2} \partial_i u_j)+ \sum^n_{i=1} u_i\partial_i u_j+ \partial_j p= h_j\quad\text{in }\Omega\times [0,T], \] \[ \text{div\,}u= 0\quad\text{in }\Omega\times [0,T]. \] For a bounded domain \(\Omega\subset\mathbb{R}^n\) \((n\in\mathbb{N})\) and for \(p_i\geq \max\{2,3,-2/n\}\) global solvability of the initial-boundary value problem (with the Dirichlet condition) is proved. For \(p_i\geq 4\) and for isotropic nonlinearity the global uniqueness of the solution is established.
reviewed by: Ibrahim Aganović
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1879979
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: bounded domain
zbMATH Keywords: global solvability
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: global uniqueness
author: K. Soltanov
MaRDI profile type: Publication
cites work: Q4002573
cites work: Q5618254
cites work: Q5890172
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cites work: Teoremi di inclusione per spazi di Sobolev non isotropi
description: scientific article; zbMATH DE number 1879979