EXISTENCE OF SOLUTIONS OF THE $g$-NAVIER-STOKES EQUATIONS

Abstract

The $g$-Navier-Stokes equations in spatial dimension 2 are the following equations introuduced in [3] $$ \frac{\partial \mathbf u}{\partial t}-\nu\Delta {\mathbf u} + (\mathbf u \cdot\nabla)\mathbf u +\nabla p =\mathbf f, $$ with the continuity equation $$ \frac{1}{g}\nabla\cdot (g {\bf u})= 0. $$ Here, we show the existence and uniqueness of solutions of $g$-Navier-Stokes equations on $\mathbf R^n$ for $n=2, 3$.