97-61 Jiahong Wu

The Complex Ginzburg-Landau Equation with Weak Initial Data (27K, Latex) Feb 11, 97

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Abstract. In this paper we investigate the existence and regularity of the solutions to the complex Ginzburg-Landau equation, $\partial_t u = Au +(a+i\nu)\Delta u -(b+i\mu)|u|^{2\sigma}u$, on the phase space $L_{r,p}({\Bbb R}^n)$ of weighted $L^p$ functions in infinite domain ${\Bbb R}^n$ of arbitrary spatial dimensions. The unique local strong solutions are established for subcritical $\sigma$, i.e., $r>\frac{n}{p}-\frac{1}{\sigma}$. Especially, the classical Lebesgue phase space $L^p$ and the Hilbert phase space $H^r$ are included.

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