Global Existence of Smooth Solutions to the Incompressible 2D Navier-Stokes-Landau-Lifshitz Equations with the Dzyaloshinskii-Moriya Interaction and V-Flow Term

Abstract

The paper focuses on the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations, incorporating the Dzyaloshinskii-Moriya (DM) interaction and a V-flow term, derived as models for magnetovi-scoelastic materials. It is demonstrated that under assumption small initial data there exist the global smooth solutions for this coupled system posed on T² or R² .