Regularity results of solution uniform in time for complex Ginzburg-Landau equation

We provide the H²-regularity result of the solution ψ and its first- order time derivative ψ_t and the second-order time derivative ψ_tt for the complex Ginzburg-Landau equation with the Dirichlet or Neumann boundary conditions. The analysis shows that these regularity results are uniform when t tends to ∞ and 0 and are dependent of the powers of ε⁻¹.