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

doi:10.1007/s10483-018-2380-8

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (10): 1499-1528.doi: https://doi.org/10.1007/s10483-018-2380-8

• 论文 • 上一篇

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

Ruiying WEI¹, Yin LI¹, Zheng'an YAO²

1. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, Guangdong Province, China;
2. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

收稿日期:2017-12-14 修回日期:2018-05-30 出版日期:2018-10-01 发布日期:2018-10-01
通讯作者: Yin LI E-mail:liyin2009521@163.com
基金资助:
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)

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

Ruiying WEI¹, Yin LI¹, Zheng'an YAO²

1. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, Guangdong Province, China;
2. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received:2017-12-14 Revised:2018-05-30 Online:2018-10-01 Published:2018-10-01
Contact: Yin LI E-mail:liyin2009521@163.com
Supported by:
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)

摘要/Abstract

摘要： 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).

关键词: Navier-Stokes-Landau-Lifshitz system, stiffened shell of revolution, torispherical shell, uniform externalpressure, plastic buckling, Fourier-splitting method, decay rate

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).

Key words: Navier-Stokes-Landau-Lifshitz system, stiffened shell of revolution, torispherical shell, uniform externalpressure, plastic buckling, Fourier-splitting method, decay rate

中图分类号:

Ruiying WEI, Yin LI, Zheng'an YAO. Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(10): 1499-1528.

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

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

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