Jiahong Wu
The Inviscid Limit of the Complex Ginzburg-Landau Equation
(45K, Latex)
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 ${\Bbb R}^n$.