On absorbing set for 3D Maxwell--Schrödinger damped driven equations in bounded region

Abstract

We consider the 3D damped driven Maxwell--Schrödinger equations in a bounded region under suitable boundary conditions. We establish new a priori estimates, which provide the existence of global finite energy weak solutions and bounded absorbing set. The proofs rely on the Sobolev type estimates for magnetic Schrödinger operator.

10 pages, 0 figures

References in corpus (3)

• Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schrödinger system
• Effective dynamics for solitons in the nonlinear Klein Gordon Maxwell system and the Lorentz force law
• On global attractors for 2D damped driven nonlinear Schrödinger equations