Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations
Analysis of PDEs
2016-01-26 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1601.06178,
title = {Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations},
author = {Hakima Bessaih and Saber Trabelsi and Hamdi Zorgati},
journal= {arXiv preprint arXiv:1601.06178},
year = {2016}
}
Comments
To appear in ESAIM: Mathematical Modelling and Numerical Analysis