Strichartz estimates and its application to the well-posedness of the nonlinear Schr\"odinger equations on H-type groups

Abstract

The aim of this article is to give the well-posedness results for the Cauchy problem of the nonlinear Schr\"odinger equation with power type nonlinearities on H-type groups. To do this, we prove the dispersive estimate and Strichartz estimate. Although these estimates are given by Hierro (2005), its complete proofs cannot be find. We correct the statement of these estimates, give the proofs, and apply to the nonlinear problem. Our well-posedness results are an improvement of the previous result by Bruno et al.