2023/07/12 by Zhang, Chenlu, Wang, Huaqiao
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2307.06022
In this paper, we mainly consider the global solvability of smooth solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation in the Morrey space. We derive the covariant complex Ginzburg-Landau equation by using moving frames to address the nonlinear parts. Applying the semigroup estimates and energy methods, we extend local classical solutions to global solutions and prove the boundedness of ‖∇\boldsymbolm‖L∞(ℝ3), where \boldsymbolm is the magnetic intensity. Moreover, we obtain a global weak solution by using an approximation result and improve the regularity of the obtained solution by the regularity theory. Finally, we establish the existence and uniqueness of global smooth solutions under some conditions on ∇\boldsymbolm0 and the density of the spin-polarized current.