Type: Article

Critical nonlinear Schrödinger equations in higher space dimensions

Hayashi, Nakao; Chunhua, LI; Naumkin, P. I.;

Abstract:

We study the critical nonlinear Schrödinger equations i?tu+12?u=?|u|2/nu,(t,x)?R+×Rn, in space dimensions n?4, where ??R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.