On global well-posedness to 3D Navier-Stokes-Landau-Lifshitz equations

In this paper, we prove the global well-posedness of solutions for the Cauchy problem of three-dimensional incompressible Navier-Stokes-Landau-Lifshitz equations under the condition that $\|u_0\|_{H^{\frac12}}+\|\nabla d_0\|_{H^{\frac12+\varepsilon}}$ ($\varepsilon>0)$ is sufficiently small. This result can be seen as an improvement of the previous paper [20].