 9761 Jiahong Wu
 The Complex GinzburgLandau Equation with Weak Initial Data
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Feb 11, 97

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Abstract. In this paper we investigate the existence and regularity of
the solutions to the complex GinzburgLandau 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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