Gevrey regularizing effect for nonlinear Schrödinger equations (Q1355276)

The paper deals with the following Cauchy problem for nonlinear Schrödinger equations in \(n\) dimensions: \[ i\partial_tu+\Delta u=f(t,x,u),\quad u(0,x)= \phi(x), \] where \(f(t,x,u)\) is a complex valued function of Gevrey class. One shows that if the initial data \(\phi\) is in some Gevrey class of order \(s\) with respect to \(x\), then the solution \(u\) is in the Gevrey class of order \(\max(s/2,1)\) with respect to \(x\). Here \(f\) is not necessarily a polynomial.