Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H~1

摘要

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