We prove the global existence of analytic solutions to nonlinear Schrödinger equation with quintic nonlinearity in n space dimensions for sufficiently small Cauchy data with exponential decay. The smallness assumption on the data is imposed in terms of the critical Sobolev space Ḣn/2-1/2. Moreover, a characterization of some class of analytic functions is given.
- Analytic smoothing effect
- Nonlinear Schrödinger equation
ASJC Scopus subject areas
- Applied Mathematics