Existence and stability of standing waves for nonlinear fractional Schrodinger equation with logarithmic nonlinearity

In this paper we consider the nonlinear fractional logarithmic Schrodinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we prove that the set of minimizers is a stable set for the initial value problem, that is, a solution whose initial data is near the set will remain near it for all time. (C) 2017 Elsevier Ltd. All rights reserved.