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
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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

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

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参考文献(16)

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