Jiahong Wu
The Complex Ginzburg-Landau Equation with Weak Initial Data
(27K, Latex)

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.