On the Cauchy problem for the nonlinear Schrodinger equations including fractional dissipation with variable coefficient

Abstract

This paper is devoted to the Cauchy problem for the nonlinear Schrodinger equation with time‐dependent fractional damping term. We prove the local existence result, and we study the global existence and blow‐up solutions.

A Note on a Damped Focusing Inhomogeneous Choquard Equation

“…In [18], M. Ohta and G. Todorova established that the Cauchy problem associated to (1.2) is well posed in the energy space and the solution is global for large damping. For other modifications of the classical equation (1.2), see also [6,7,24,25]. It is thus quite natural to complete the nonlinear Choquard equation by a linear dissipative term to take into account some dissipation phenomena.…”