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Science in China Series A: Mathematics

, Volume 46, Issue 1, pp 64–74 | Cite as

Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H1

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Abstract

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1(Rn), we shall show the asymptotic behavior for its solutions in C(0, ∖;H1(Rn)) ∩ L2(0, ∖;H1,2n/(n-2)(R2)), n≥3. Analogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥1.

Keywords

complex Ginzburg-Landau equation critical power in H1 large time decaying estimate time-space Lp-Lp’ estimate at endpoint 

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Copyright information

© Science in China Press 2003

Authors and Affiliations

  1. 1.Department of MathematicsPeking UniversityBeijingChina

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