On Blow‐Up Criteria for Incompressible Navier‐Stokes‐Landau‐Lifshitz System With Dzyaloshinskii‐Moriya Interaction and V‐Flow

ABSTRACT In this paper, we investigate the blow‐up criteria for the local smooth solutions to the incompressible Navier‐Stokes‐Landau‐Lifshitz system with Dzyaloshinskii‐Moriya term and V‐flow in . More precisely, we establish the Serrin‐type blow‐up criterion in terms of the velocity field and the gradient of the magnetization field , as well as criterion in Besov spaces with negative indices for the gradient of the velocity field and the second‐order derivatives of the magnetization field .