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Global Smooth Solution to the Incompressible Navier-Stokes-Landau-Lifshitz Equations

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Abstract

In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations. We will prove global existence of the smooth solution to the incompressible Navier-Stokes-Landau-Lifshitz equation with small initial data in \({\mathbb{T}^2}\) or ℝ2 and ℝ3.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Guang-wu Wang & You-de Wang

  2. Hua Loo-Keng Key Laboratory of Mathematics, Institute of Mathematics, AMSS and School of Mathematical Science, UCAS, Beijing, 100190, China

    You-de Wang

Authors
  1. Guang-wu Wang
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  2. You-de Wang
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Correspondence to Guang-wu Wang.

Additional information

The first author is supported by the National Natural Science Foundation of China (No.11801107), Science and Technology Projects in Guangzhou (No.202102010467), the second author is supported by the National Natural Science Foundation of China (Grant No. 11971400), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020A1515011019).

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Wang, Gw., Wang, Yd. Global Smooth Solution to the Incompressible Navier-Stokes-Landau-Lifshitz Equations. Acta Math. Appl. Sin. Engl. Ser. 39, 135–178 (2023). https://doi.org/10.1007/s10255-023-1029-8

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  • DOI: https://doi.org/10.1007/s10255-023-1029-8

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