We prove the existence of a uniform initial datum whose solution decays, in var- ious Lp spaces, at different rates along different time sequences going to infinity, for complex Ginzburg-Landau equation on RN, of various parameters θ and γ.
The authors consider the scattering phenomena of the defocusing H^s-critical NLS.It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of existence,then the solution is global and scatters.
We consider the scattering of Cauchy problem for the focusing combined power-type Schroodinger equation. In the spirit of concentration-compactness method, we will show that, H1 solution will scatter under some condition on its energy and mass. We adapt some variance argument, following the idea of Ibrahim–Masmoudi–Nakanishi.
