二维部分耗散Navier-Stokes方程解的最优代数衰减性

doi:10.3969/j.issn.0253-2778.2018.05.003

中国科学技术大学学报 ›› 2018, Vol. 48 ›› Issue (5): 361-366.DOI: 10.3969/j.issn.0253-2778.2018.05.003

二维部分耗散Navier-Stokes方程解的最优代数衰减性

张昭云，谢倩倩，贾艳，董柏青

安徽大学数学科学学院，安徽合肥 230601

收稿日期:2017-08-30 修回日期:2018-01-25 接受日期:2018-01-25 出版日期:2018-05-31 发布日期:2018-01-25
通讯作者: 董柏青
作者简介:张昭云,男,1992年生,硕士生.研究方向:偏微分方程. E-mail:zhangzhaoyunmath@163.com
基金资助:
国家自然科学基金(11271019,11571240)资助.

Optimal algebraic decay of solutions for 2D Navier-Stokes equations with partial dissipation

ZHANG Zhaoyun, XIE Qianqian, JIA Yan, DONG Boqing

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2017-08-30 Revised:2018-01-25 Accepted:2018-01-25 Online:2018-05-31 Published:2018-01-25

摘要/Abstract

摘要： 主要讨论部分耗散二维Navier-Stokes方程解的时间衰减性.利用改进的Fourier分解方法和归纳方法,得到了方程解及其高阶导数的最优代数衰减率‖su(t)‖L2≤c(1+t)-s+12, s≥0, t>0|..

关键词: Navier-Stokes方程, 部分耗散, Fourier 分解方法, 最优代数衰减

Abstract: The optimal algebraic decay of solutions for two-dimensional Navier-Stokes equation with partial dissipation was studied. By developing the classic Fourier splitting methods together with inductive methods, the higher-order derivatives of solutions in the optimal algebraic rates was obtained.

Key words: Navier-Stokes equations, partial dissipation, Fourier splitting methods, optimal algebraic decay

中图分类号:

O175.2

张昭云，谢倩倩，贾艳，董柏青. 二维部分耗散Navier-Stokes方程解的最优代数衰减性[J]. 中国科学技术大学学报, 2018, 48(5): 361-366.

ZHANG Zhaoyun, XIE Qianqian, JIA Yan, DONG Boqing. Optimal algebraic decay of solutions for 2D Navier-Stokes equations with partial dissipation[J]. Journal of University of Science and Technology of China, 2018, 48(5): 361-366.

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二维部分耗散Navier-Stokes方程解的最优代数衰减性

Optimal algebraic decay of solutions for 2D Navier-Stokes equations with partial dissipation

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