Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations

TL;DR

This paper proves the global existence and uniqueness of solutions for a modified 3D anisotropic Navier-Stokes model that includes a nonlinear power term, relevant for porous media flows, without small initial data assumptions.

Contribution

It introduces a modified anisotropic Navier-Stokes model with a nonlinear term and establishes global well-posedness results without smallness constraints on initial data.

Findings

Global existence of solutions proven

Uniqueness of solutions established

No small initial data assumption required

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.