Some nonexistence results for space-time fractional Schrödinger equations without gauge invariance

2021/10/05 by Kirane, Mokhtar, Fino, Ahmad Z.
#26A33 #35A01 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.01797

Abstract

In this paper, we consider the Cauchy problem in ℝ^N, N≥1, for semi-linear Schrödinger equations with space-time fractional derivatives. We discuss the nonexistence of global L¹ or L² weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local L¹ or L² weak solutions in the supercritical case are studied.

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