## Taiwanese Journal of Mathematics

### 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 $n=2, 3$.

#### Article information

Source
Taiwanese J. Math., Volume 8, Number 1 (2004), 85-102.

Dates
First available in Project Euclid: 20 July 2017

https://projecteuclid.org/euclid.twjm/1500558459

Digital Object Identifier
doi:10.11650/twjm/1500558459

Mathematical Reviews number (MathSciNet)
MR2058920

Zentralblatt MATH identifier
1060.35103

Subjects
Bae, Hyeong-Ohk; Roh, Jaiok. EXISTENCE OF SOLUTIONS OF THE $g$-NAVIER-STOKES EQUATIONS. Taiwanese J. Math. 8 (2004), no. 1, 85--102. doi:10.11650/twjm/1500558459. https://projecteuclid.org/euclid.twjm/1500558459