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二维Navier—Stokes方程组的H1一致吸引子
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]温州大学数学与信息科学学院,浙江温州325035
  • 相关基金：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
作者： 赵才地[1]
关键词： 一致吸引子, 非自治Navier-Stokes方程组, 渐近光滑效应, Uniform attractor, Nonautonoraous Navier-Stokes equations, Asymptotic smoothing effect.
中文摘要：

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．．

英文摘要：

This paper is concerned with the existence of uniform attractor and asymptotic smoothing effect of solutions for two-dimensional （2D） nonautonomous Navier-Stokes equa- tions 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 Hi-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.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:5382