Finite time extinction for nonlinear Schrodinger equation in 1D and 2D

Abstract

We consider a nonlinear Schrodinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.

18 pages

References in corpus (2)

• On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
• Madelung, Gross-Pitaevskii and Korteweg

Cited by in corpus (4)

• A note on the nonlinear Schrödinger equation in a general domain
• Finite time extinction for the strongly damped nonlinear Schr{ö}dinger equation in bounded domains
• Finite time extinction for a class of damped Schr{ö}dinger equations with a singular saturated nonlinearity
• A conservation law with spatially localized sublinear damping