Local regularity of solutions to nonlinear Schrödinger equations (Q915963)

The nonlinear Schrödinger equation i \(\partial u/\partial t=-\Delta u+F(u)\), \(t\geq 0\), \(x\in {\mathbb{R}}^ n\), is studied. Here \(\Delta\) denotes the Laplace operator in the x-variable and \(F(u)(x,t)=F(u(x,t))\). Results are given for the local regularity of the solution u when \(u(x,0)=f(x)\) and f belongs to \(H_ 1({\mathbb{R}}^ n)\) or \(H_ 2({\mathbb{R}}^ n)\).