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.
Citation
Jaiok Roh. "CONVERGENCE OF THE g-NAVIER-STOKES EQUATIONS." Taiwanese J. Math. 13 (1) 189 - 210, 2009. https://doi.org/10.11650/twjm/1500405278
Information