二维Navier-Stokes 方程组的H1 一致吸引子

数学物理学报 ›› 2011, Vol. 31 ›› Issue (5): 1416-1430.

二维Navier-Stokes 方程组的H¹ 一致吸引子

赵才地

温州大学数学与信息科学学院 |浙江温州 325035

收稿日期:2009-10-27 修回日期:2010-09-21 出版日期:2011-10-25 发布日期:2011-10-25
基金资助:
国家自然科学基金(10901121, 10826091, 10771139)、浙江省自然科学基金 (Y6080077)、中国博士后科学基金(20090460952)、温州大学预研基金(2008YYLQ01)和浙江省高校优秀青年教师及温州市551人才工程资助

H¹-uniform Attractor for 2D Navier-Stokes Equations

ZHAO Cai-De

Department of Mathematics and Information Science, Wenzhou University, Zhejiang Wenzhou 325035

Received:2009-10-27 Revised:2010-09-21 Online:2011-10-25 Published:2011-10-25
Supported by:
国家自然科学基金(10901121, 10826091, 10771139)、浙江省自然科学基金 (Y6080077)、中国博士后科学基金(20090460952)、温州大学预研基金(2008YYLQ01)和浙江省高校优秀青年教师及温州市551人才工程资助

摘要/Abstract

摘要：

该文讨论一类非自治Navier-Stokes方程组在二维区域(有界或无界)上一致吸引子的存在性与解的渐近光滑效应. 作者应用拟能方程得到Navier-Stokes方程组生成的一簇过程的渐近紧性, 并证明H¹一致吸引子的存在性. 之后, 作者证明了L²一致吸引子属于H¹一致吸引子, 从而在``解最终变得比初值光滑"的意义下揭示了Navier-Stokes方程组解的渐近光滑效应.

关键词: 一致吸引子, , 非自治Navier-Stokes方程组, 渐近光滑效应

Abstract:

This paper is concerned with the existence of uniform attractor and asymptotic smoothing effect of solutions for two-dimensional (2D) nonautonomous Navier-Stokes equations in 2D domains (bounded or not). The author uses the enstrophy equation to obtain the asymptotic compactness of the family of processes associated with the Navier-Stokes equations and establishes the existence of H¹-uniform attractor and thus reveal the asymptotic smoothing effect of the solutions in the sense that the solutions become eventually more
regular than the initial data.

Key words: Uniform attractor, Nonautonomous Navier-Stokes equations, Asymptotic smoothing effect

中图分类号:

35B40

赵才地. 二维Navier-Stokes 方程组的H¹ 一致吸引子[J]. 数学物理学报, 2011, 31(5): 1416-1430.

ZHAO Cai-De. H¹-uniform Attractor for 2D Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2011, 31(5): 1416-1430.

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二维Navier-Stokes 方程组的H¹ 一致吸引子

H¹-uniform Attractor for 2D Navier-Stokes Equations

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