Anisotropically diffused and damped Navier-Stokes equations

Hermenegildo Borges de  Oliveira

doi:10.3934/proc.2015.0349

Article Contents

2015, Volume 2015: 349-358. Doi: 10.3934/proc.2015.0349 open access

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Anisotropically diffused and damped Navier-Stokes equations

Hermenegildo Borges de Oliveira^1,

1.
FCT - Universidade do Algarve, Campus de Gambelas, 8005-139 Faro

Received: September 2014

Revised: February 2015

Published: October 2015

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Abstract

The incompressible Navier-Stokes equations with anisotropic diffusion and anisotropic damping is considered in this work. For the associated initial-boundary value problem, we prove the existence of weak solutions and we establish an energy inequality satisfied by these solutions. We prove also under what conditions the solutions of this problem extinct in a finite time.

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Mathematics Subject Classification: Primary: 35Q35, 35D30, 35B40; Secondary: 76D05, 76D03.

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