Local well-posedness of the nonlinear Schrödinger equations on the sphere for data in modulation spaces

Abstract

In this paper we discuss a priori estimates derived from the energy method to the initial value problem for the cubic nonlinear Schrödinger on the sphere $S^2$. Exploring suitable a priori estimates, we prove the existence of solution for data whose regularity is $s=1/4$.

17 pages

References in corpus (1)

• Bilinear Eigenfunction Estimates and the Nonlinear Schroedinger Equation on Surfaces