Communications in Mathematical Sciences

Volume 22 (2024)

Number 4

Existence and uniqueness of smooth solutions for the high-order Landau-Lifshitz type systems

Pages: 961 – 976

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n4.a4

Authors

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Ying Zhang (The Graduate School of China Academy of Engineering Physics, Beijing, China)

Abstract

This paper mainly discusses the existence and uniqueness of solutions for the high-order Landau-Lifshitz type systems. Firstly, we consider the periodic initial value problem for the fourth-order Landau-Lifshitz type equation. Then we explore the existence and uniqueness of a global smooth solution for the high-order Landau-Lifshitz type equation. The proof is based on the technique of finite difference-differential methods and the \textit{a priori} estimates.

Keywords

Landau-Lifshitz type systems, existence and uniqueness, smooth solution

2010 Mathematics Subject Classification

35B65, 35Q60

Full Text (PDF format)

Received 21 May 2023

Received revised 2 September 2023

Accepted 1 October 2023

Published 12 July 2024