## Taiwanese Journal of Mathematics

### CONVERGENCE OF THE g-NAVIER-STOKES EQUATIONS

Jaiok Roh

#### Abstract

The 2D $g$-Navier-Stokes equations have the following form, $$\frac{\partial \mathbf u}{\partial t}-\nu\Delta { \mathbf u} + ( \mathbf u \cdot\nabla)\mathbf u +\nabla p = {\bf f}, \ \ \mbox{in} \ \Omega$$ with the continuity equation $$\nabla\cdot (g {\mathbf u})= 0, \ \ \mbox{in} \ \Omega,$$ where $g$ is a smooth real valued function. We get the Navier-Stokes equations, for $g$ = $1$. In this paper, we investigate solutions $\{\mathbf u_g, p_g\}$ of the $g$-Navier-Stokes equations, as $g \to 1$ in some suitable spaces.

#### Article information

Source
Taiwanese J. Math., Volume 13, Number 1 (2009), 189-210.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405278

Digital Object Identifier
doi:10.11650/twjm/1500405278

Mathematical Reviews number (MathSciNet)
MR2489313

Zentralblatt MATH identifier
1179.35224

#### Citation

Roh, Jaiok. CONVERGENCE OF THE g-NAVIER-STOKES EQUATIONS. Taiwanese J. Math. 13 (2009), no. 1, 189--210. doi:10.11650/twjm/1500405278. https://projecteuclid.org/euclid.twjm/1500405278

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