97-114 Jiahong Wu

The Inviscid Limit of the Complex Ginzburg-Landau Equation (45K, Latex) Mar 10, 97

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Abstract. In this paper we investigate the inviscid limit (as $a,b\to 0$) of the complex Ginzburg-Landau (CGL) equation, $\partial_t u=(a+i\nu)\Delta u -(b+i\mu)|u|^{2\sigma}u$, on the whole space of arbitrary spatial dimension $n$. We establish global (in time) inviscid limit results in $L^2, L^{2\sigma+2}$ and $H^1$. The $H^1$ result became possible after Ginibre and Velo obtained the existence of $H^1$ solutions for the CGL equation on ${\Bbb R}^n$.

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