The Complex Ginzburg-Landau Equation with Weak Initial Data
نویسنده
چکیده
In this paper we investigate the existence and regularity of the solutions to the complex Ginzburg-Landau equation, @ t u = Au + (a + ii))u ? (b + ii)juj 2 u, on the phase space L r;p (R n) of weighted L p functions in innnite domain R n of arbitrary spatial dimensions. The unique local strong solutions are established for subcritical , i.e., r > n p ? 1. Especially, the classical Lebesgue phase space L p and the Hilbert phase space H r are included.
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