A Remark on Regularity for the Axisymmetric Navier-Stokes Equations

XIE Hong-yan; LI Jie; HE Fang-yi

doi:10.21656/1000-0887.370192

Volume 38 Issue 3

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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

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

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A Remark on Regularity for the Axisymmetric Navier-Stokes Equations

doi: 10.21656/1000-0887.370192

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)

Received Date: 2016-06-21
Rev Recd Date: 2016-10-16
Publish Date: 2017-03-15

Abstract

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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References(16)

References

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