Global attractor for damped forced nonlinear logarithmic Schrödinger equations

Abstract

We consider here a damped forced nonlinear logarithmic Schrödinger equation in R N . We prove the existence of a global attractor in a suitable energy space. We complete this article with some open issues for nonlinear logarithmic Schrödinger equations in the framework of infinitedimensional dynamical systems.

Non-linear Smoothing for the Periodic Generalized Non-linear Schrödinger Equation

“…x (R) global attractor in H 2 x (R). There is more known on the real line, where several recent results by Goubet [20,21] showed the existence of a global attractor in H α x (R) for the cubic fractional NLS with spatial derivative term (−△) α u for α ∈ (− 1 2 , 1] and in a subset of H 1 x (R) for the NLS with nonlinearity u(log |u|) 2 . Of additional interest is a result of Tao [31], where the existence of a global attractor in the subset of spherically symmetric functions in H 1…”