Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations∗,∗∗
1 University of Wyoming, Department of Mathematics, Dept. 3036,
1000 East University Avenue, Laramie WY 82071, US.
2 Division of Mathematical and Computer Science and Engineering, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Saudi Arabia.
3 Département de Mathématiques, Campus Universitaire, Université Tunis El Manar 2092, Tunisia.
Revised: 19 October 2015
Accepted: 22 January 2016
We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.
Mathematics Subject Classification: 35Q30 / 35Q35 / 76D05 / 76D03 / 76S05
Key words: Navier−Stokes equations / Brinkman−Forchheimer-extended Darcy model / anisotropic viscosity
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