(untitled) (Journal of Partial Differential Equations, 2020)
In this paper, we study the limit behavior of self-similar solutions for the Complex Ginzburg-Landau (CGL) equation in the nonstandard function space E_s,p. We prove the uniform existence of the solutions for the CGL equation and its limit equation in E_s,p. Moreover we show that the self-similar solutions of CGL equation converge, globally in time, to those of its limit equation as the parameters tend to zero. Key Words Ginzburg-Landau equation; Schrödinger equation; self-similar solution; limit behavior.