Anisotropically diffused and damped Navier-Stokes equations

Pages: 349 - 358, Volume 2015, Issue special, November 2015      doi:10.3934/proc.2015.0349

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Hermenegildo Borges de Oliveira - FCT - Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal (email)

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.

Keywords:  Navier-Stokes, anisotropic diff usion, anisotropic damping, existence, extinction in a fi nite time.
Mathematics Subject Classification:  Primary: 35Q35, 35D30, 35B40; Secondary: 76D05, 76D03.

Received: September 2014;      Revised: February 2015;      Available Online: November 2015.