The nonexistence of global solutions for a time fractional nonlinear Schrodinger equation without gauge invariance

In this paper, we study the following time fractional Schrodinger equation i(0)(alpha)(C) D-t(alpha) u + Delta u = lambda vertical bar u vertical bar(p), x is an element of R-N, t is an element of [0,T), where 0 < alpha < 1, i(alpha) denotes the principal value of i(alpha), T > 0, lambda is an element of C \ {0}, p > 1, u(t, x) is a complex -valued function, and Pru denotes Caputo fractional derivative of order a. We prove that the problem admits no global weak solution with suitable initial data when 1 < p < 1 + 2/N by using the test function method, and also give some conditions which imply the problem has no global weak solution for every p > 1. (C) 2016 Elsevier Ltd. All rights reserved.