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Anisotropically diffused and damped Navier-Stokes equations

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

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