留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

海洋动力学中二维黏性原始方程组解对热源的收敛性

李远飞

李远飞. 海洋动力学中二维黏性原始方程组解对热源的收敛性[J]. 应用数学和力学, 2020, 41(3): 339-352. doi: 10.21656/1000-0887.400176
引用本文: 李远飞. 海洋动力学中二维黏性原始方程组解对热源的收敛性[J]. 应用数学和力学, 2020, 41(3): 339-352. doi: 10.21656/1000-0887.400176
LI Yuanfei. Convergence Results on Heat Source for 2D Viscous Primitive Equations of Ocean Dynamics[J]. Applied Mathematics and Mechanics, 2020, 41(3): 339-352. doi: 10.21656/1000-0887.400176
Citation: LI Yuanfei. Convergence Results on Heat Source for 2D Viscous Primitive Equations of Ocean Dynamics[J]. Applied Mathematics and Mechanics, 2020, 41(3): 339-352. doi: 10.21656/1000-0887.400176

海洋动力学中二维黏性原始方程组解对热源的收敛性

doi: 10.21656/1000-0887.400176
基金项目: 广东省普通高校特色创新类项目(2018KTSCX332);广东省自然科学基金(2017A030313037)
详细信息
    作者简介:

    李远飞(1982—), 博士, 特聘教授(E-mail: liqfd@163.com).

  • 中图分类号: O178

Convergence Results on Heat Source for 2D Viscous Primitive Equations of Ocean Dynamics

  • 摘要: 考虑了在一个柱形区域上的海洋动力学中二维黏性方程组解的收敛性.在此模型中存在一个关键的参数就是热源,众多周知,它的存在可能会使流体内层之间出现共振从而导致不稳定.因此,通过推导方程组的先验界,得到了方程组的解对热源自身的收敛性.
  • [1] RICHARDSON L F. Weather Prediction by Numerical Press [M]. Cambridge: Cambridge University Press, 1922.
    [2] 郭柏灵, 黄代文, 黄春研. 大气、海洋动力学中一些非线性偏微分方程的研究[J]. 中国科学: 物理学 力学 天文学, 2014,44(12): 1275-1285.(GUO Boling, HUANG Daiwen, HUANG Chunyan. Study on some partial differential equations in the atmospheric and oceanic dynamics[J]. Scientia Sinica: Physica, Mechanica & Astronomica,2014,44(12): 1275-1285.(in Chinese))
    [3] ZENG Q C. Mathematical and Physical Basis of Numerical Weather Prediction [M]. Beijing: Science Press, 1979.
    [4] LIONS J L, TEMAM R, WANG S. New formulations of the primitive equations of atmosphere and applications[J]. Nonlinearity,1992,〖STHZ〗 5: 237-288.
    [5] LIONS J, TEMAM R, WANG S. On the equations of the large-scale ocean[J]. Nonlinearity,1999,5: 1007-1053.
    [6] SUN J Y, CUI S B. Sharp well-posedness and ill-posedness of the three-dimensional primitive equations of geophysics in Fourier-Besov spaces[J]. Nonlinear Analysis: Real World Applications,2019,4: 445-465.
    [7] HIEBER M, HUSSEIN A, KASHIWABARA T. Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion[J]. Journal of Differential Equations,2016,261(12): 6950-6981.
    [8] YOU B, LI F. Global attractor of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics[J]. Zeitschrift für Angewandte Mathematik und Physik,2018,69: 114. DOI: 10.1007/s00033-018-1007-9.
    [9] CHIODAROLI E, MICHLEK M. Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations[J]. Communications in Mathematical Physics,2017,353: 1201-1216.
    [10] SUN J Y, YANG M. Global well-posedness for the viscous primitive equations of geophysics[J]. Boundary Value Problems,2016,2016: 21. DOI: 10.1186/s13661-016-0526-6.
    [11] SUN J Y, CUI S B. Sharp well-posedness and ill-posedness of the three-dimensional primitive equations of geophysics in Fourier-Besov spaces[J]. Nonlinear Analysis: Real World Applications,2019,48: 445-465.
    [12] GUO B L, HUANG D W. On the 3D viscous primitive equations of the large-scale atmosphere[J]. Acta Mathematica Scientia,2009,29(4): 846-866.
    [13] 李振邦. 一类非局部Cahn-Hilliard方程弱解的存在唯一性[J]. 纯粹数学与应用数学, 2019,35(1): 15-33.(LI Zhenbang. The existence and uniqueness of solutions for a nonlocal convextive Cahn-Hilliard equation[J]. Pure and Applied Mathematics,2019,35(1): 15-33.(in Chinese))
    [14] 王欣, 郭科. 一类非凸优化问题广义交替方向法的收敛性[J]. 应用数学和力学, 2018,39(12): 1410-1425.(WANG Xin, GUO Ke. Convergence of the generalized alternating direction method of multipliers for a class of nonconvex optization problrms[J]. Applied Mathematics and Mechanics,2018,39(12): 1410-1425.(in Chinese))
    [15] HIRSCH M W, SMALE S. Differential Equations, Dynamical Systems and Linear Algebra [M]. New York: Academic Press, 1974.
    [16] AMES K A, STRAUGHAN B. Non-Standard and Improperly Posed Problems [M]. Mathematics in Science and Engineering Series : Vol94. San Diego: Academic Press, 1997.
    [17] LIU Y. Continuous dependence for a thermal convection model with temperature-dependent solubitity[J]. Applied Mathematics and Computation,2017,308: 18-30.
    [18] LIU Y, XIAO S, LIN C. Continuous dependence for the Brinkman-Forchheimer fluid interfacing with a Darcy fluid in a bounded domain[J]. Mathematics and Computers in Simulation,2018,150: 66-82.
    [19] LIU Y, DU Y, LIN C. Convergence results for Forchheimer’s equations for fluid flow in porous media[J]. Journal of Mathematical Fluid Mechanics,2010,12(4): 576-593.
    [20] SCOTT N L. Continuous dependence on boundary reaction terms in a porous medium of Darcy type[J]. Journal of Mathematical Analysis and Applications,2013,399: 667-675.
    [21] SCOTT N L, STRAUGHAN B. Continuous dependence on the reaction terms in porous convection with surface reactions[J]. Quarterly of Applied Mathematics,2013,71: 501-508.
    [22] LI Y, LIN C. Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe[J]. Applied Mathematics and Computation,2014,244: 201-208.
    [23] HAMEED A A, HARFASH A J. Continuous dependence of double diffusive convection in a porous medium with temperature-dependent density[J].Basrah Journal of Science,2019,37: 1-15.
    [24] CAO C, TITI E S. Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics[J]. Annals of Mathematics,2007,166: 245-267.
    [25] 黄代文, 郭柏灵. 关于海洋动力学中二维的大尺度原始方程组[J]. 应用数学和力学, 2007,28(5): 521-531.(HUANG D W, GUO B L. On two-dimensional large-scale primitive equations in oceanic dynamics[J]. Applied Mathematics and Mechanics,2007,28(5): 521-531.(in Chinese))
    [26] 黄代文, 郭柏灵. 关于海洋动力学中二维的大尺度原始方程组[J]. 应用数学和力学, 2018,28(5): 532-538.(HUANG Daiwen, GUO Boling. On two-dimensional large-scale primitive equations in oceanic dynamics[J]. Applied Mathematics and Mechanics,2007,28(5): 532-538.(in Chinese))
    [27] HARDY C H, LITTLEWOOD J E, POLYA G. Inequalities [M]. Cambridge: Cambridge University Press, 1953.
    [28] MITRONOVIC D S. Analytical Inequalities [M]. Springer-Verlag, 1970.
  • 加载中
计量
  • 文章访问数:  399
  • HTML全文浏览量:  27
  • PDF下载量:  286
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-05-30
  • 修回日期:  2019-07-22
  • 刊出日期:  2020-03-01

目录

    /

    返回文章
    返回