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Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system

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Abstract

In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek (SCHONBEK, M. E. L2 decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222 (1985)) under an additional assumption that the initial perturbation is bounded in L1(ℝ3).

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Acknowledgements

We would like to express our sincere thanks to Academician Boling GUO of Institute of Applied Physics and Computational Mathematics in Beijing for his fruitful help and discussion.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaoguan University, Shaoguan, 512005, Guangdong Province, China

    Ruiying Wei & Yin Li

  2. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Zheng’an Yao

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  1. Ruiying Wei
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  2. Yin Li
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  3. Zheng’an Yao
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Correspondence to Yin Li.

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Citation: WEI, R. Y., LI, Y., and YAO, Z. A. Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system. Applied Mathematics and Mechanics (English Edition), 39(10), 1499–1528 (2018) https://doi.org/10.1007/s10483-018-2380-8

Project supported by the National Natural Science Foundation of China (Nos. 11501373, 11701380, and 11271381), the Natural Science Foundation of Guangdong Province (Nos. 2017A030307022, 2016A030310019, and 2016A030307042), the Guangdong Provincial Culture of Seedling of China (No. 2013LYM0081), the Education Research Platform Project of Guangdong Province (No. 2014KQNCX208), and the Education Reform Project of Guangdong Province (No. 2015558)

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Wei, R., Li, Y. & Yao, Z. Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system. Appl. Math. Mech.-Engl. Ed. 39, 1499–1528 (2018). https://doi.org/10.1007/s10483-018-2380-8

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  • DOI: https://doi.org/10.1007/s10483-018-2380-8

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