Global existence and asymptotic behavior of small solutions to nonlinear Schrödinger equations in 3D. (English) Zbl 1212.35451

A nonlinear Schrödinger equation is studied. It is shown that for the solution \(u=u(x,t)\) there exists a unique state \(u_{\infty }\) such that \[ \| u(t) - \text{e}^{\frac {\text{i}t}{2}}u_{\infty }\| _{L^2} \leq Ct^{-\frac {5}{4}} \] for a small initial condition \(u_0\), \(\text{i}\) being the complex unit.


35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs