Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass

2017/06/26 by Correia, Simão
#35A01 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08475

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation on ℝ^d, where the initial data is in H¹(ℝ^d)∩ L^p(ℝ^d). We prove local well-posedness for large ranges of p and discuss some global well-posedness results.

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