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关于轴对称Navier-Stokes方程正则性的一个注记

谢洪燕 李杰 贺方毅

谢洪燕, 李杰, 贺方毅. 关于轴对称Navier-Stokes方程正则性的一个注记[J]. 应用数学和力学, 2017, 38(3): 276-283. doi: 10.21656/1000-0887.370192
引用本文: 谢洪燕, 李杰, 贺方毅. 关于轴对称Navier-Stokes方程正则性的一个注记[J]. 应用数学和力学, 2017, 38(3): 276-283. doi: 10.21656/1000-0887.370192
XIE Hong-yan, LI Jie, HE Fang-yi. A Remark on Regularity for the Axisymmetric Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2017, 38(3): 276-283. doi: 10.21656/1000-0887.370192
Citation: XIE Hong-yan, LI Jie, HE Fang-yi. A Remark on Regularity for the Axisymmetric Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2017, 38(3): 276-283. doi: 10.21656/1000-0887.370192

关于轴对称Navier-Stokes方程正则性的一个注记

doi: 10.21656/1000-0887.370192
基金项目: 国家自然科学基金(71102145)
详细信息
    作者简介:

    谢洪燕(1983—),女,副教授,博士(通讯作者. E-mail: xiehongyan@swufe.edu.cn).

  • 中图分类号: O175.29

A Remark on Regularity for the Axisymmetric Navier-Stokes Equations

Funds: The National Natural Science Foundation of China(71102145)
  • 摘要: 建立了一个关于轴对称不可压Navier-Stokes系统的正则性准则.证明了如果局部的轴对称光滑解u满足‖ωrLα1((0,T);Lβ1)+‖ωθ/r‖Lα2((0,T);Lβ2)<∞,其中2/α1+3/β1≤1+3/β1,2/α2+3/β2≤2和β1≥3, β2>3/2,那么此强解将保持光滑性直至时刻T.
  • [1] Ali A, Asghar S, Alisulami H H. Oscillatory flow of second grade fluid in cylindrical tube[J]. Applied Mathematics and Mechanics (English Edition),2013,34(9): 1097-1106.
    [2] Buske D, Bodmann B, Vilhena M T M B, et al. On the solution of the coupled advection-diffusion and Navier-Stokes equations[J]. American Journal of Environmental Engineering,2015,5(1A):1-8.
    [3] 刘莹, 章德发, 毕勇强, 等. 主动脉弓及分支血管内非稳态血流分析[J]. 应用数学和力学, 2015,36(4): 432-439.(LIU Ying, ZHANG De-fa, BI Yong-qiang, et al. Analysis of unsteady blood flow in the human aortic bifurcation[J]. Applied Mathematics and Mechanics,2015,36(4): 432-439.(in Chinese))
    [4] Constantin P, Foias C. Navier-Stokes Equations (Chicago Lectures in Mathematics) [M]. Chicago: University of Chicago Press, 1988.
    [5] Fefferman C L. Existence and smoothness of the Navier-Stokes equation[M]// The Millennium Prize Problems . Cambridge: Clay Mathematics Institute, 2006: 57-67.
    [6] Majda A J, Bertozzi A L. Vorticity and Incompressible Flow (Cambridge Texts in Applied Mathematics) [M]. Cambridge: Cambridge University Press, 2002.
    [7] Leonardi S, Málek J, Necas J, et al. On axially symmetric flows in R3[J].Z Anal Anwendungen,1999,18(3): 639-649.
    [8] Ukhovskii M R, Yudovich V I. Axially symmetric flows of ideal and viscous fluids filling the whole space[J]. Prikl Mat Meh,1968,32(1): 59-69.
    [9] Chae D, Lee J. On the regularity of the axisymmetric solutions of the Navier-Stokes equations[J]. Mathematische Zeitschrift,2002,239(4): 645-671.
    [10] Kubica A, Pokorn M, Zajaczkowski W. Remarks on regularity criteria for axially symmetric weak solutions to the Navier-Stokes equations[J]. Mathematical Methods in the Applied Sciences,2012,35(3): 360-371.
    [11] Neustupa J, Pokorn M. Axisymmetric flow of Navier-Stokes fluid in the whole space with non-zero angular velocity component[J]. Mathematica Bohemica,2001,126(2): 469-481.
    [12] ZHOU Yong. On regularity criteria in terms of pressure for the Navier-Stokes equations in R3[J]. Proc Amer Math Soc,2006,134: 149-156.
    [13] JIA Xuan-ji, ZHOU Yong. Remarks on regularity criteria for the Navier-Stokes equations via one velocity component[J]. Nonlinear Analysis: Real World Applications,2014,15: 239-245.
    [14] ZHOU Yong. A new regularity criterion for weak solutions to the Navier-Stokes equations[J]. Journal de Mathématiques Pures et Appliquées,2005,84(11): 1496-1514.
    [15] ZHOU Yong, Pokorn M. On the regularity of the solutions of the Navier-Stokes equations via one velocity component[J]. Nonlinearity,2010,23(5): 1097-1107.
    [16] ZHOU Yong. A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity[J]. Monatshefte für Mathematik,2005,144(3): 251-257.
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出版历程
  • 收稿日期:  2016-06-21
  • 修回日期:  2016-10-16
  • 刊出日期:  2017-03-15

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