Taiwanese Journal of Mathematics


Jaiok Roh

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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

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

First available in Project Euclid: 18 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C35 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]
Secondary: 35K55: Nonlinear parabolic equations

$g$-Navier-Stokes equation weak solution strong solution convergence


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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