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

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

¹西南财经大学经济学院, 成都 611130;²四川省委党校公共管理教研部, 成都 610000;³西南财经大学金融学院, 成都 611130

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
计量
- 文章访问数: 977
- HTML全文浏览量: 137
- PDF下载量: 458
- 被引次数: 0
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

A Remark on Regularity for the Axisymmetric Navier-Stokes Equations

¹School of Economics, Southwestern University of Finance and Economics, Chengdu 611130, P.R.China;²Department of Public Administration, Sichuan Administration Institute, Chengdu 610000, P.R.China;³School of Finance, Southwestern University of Finance and Economics, Chengdu 611130, P.R.China

Funds: The National Natural Science Foundation of China(71102145)

摘要

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‖ω^r‖_{Lα1((0,T);Lβ1)}+‖ω^θ/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.
- Navier-Stokes方程 /
- 轴对称流 /
- 爆破准则
Abstract: A regularity criterion for the axisymmetric incompressible NavierStokes system was established.It is proved that, if local axisymmetric smooth solution u satisfies‖ω^r‖_{Lα1((0,T);Lβ1})+‖ω^θ/r‖_{Lα2((0,T);Lβ2}))<∞,where 2/α₁+3/β₁≤1+3/β₁,2/α₂+3/β₂≤2 and β₁≥3, β₂> 3/2,this strong solution will keep its smoothness up to time T.
- Navier-Stokes equations /
- axisymmetric flow /
- blow-up criterion

HTML全文

参考文献(16)

[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.