We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.
- Analytic smoothing effect
- Global solutions
- Nonlinear Schrödinger equations
ASJC Scopus subject areas
- Applied Mathematics