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Results in Mathematics

, 74:134 | Cite as

Regularity Criteria for the Axisymmetric Navier–Stokes System with Negative Weights

  • Zujin ZhangEmail author
Article
  • 106 Downloads

Abstract

As is well-known, for the axisymmetric Navier–Stokes equations, \(ru^{\theta }\) obeys a maximal principle, \(\left\| ru^{\theta }(t)\right\| _{L^\infty } \leqslant \left\| ru^{\theta }_0\right\| _{L^\infty }\). Utilizing this fact, we can establish some more weighted regularity criteria involving \(u^r\) (\(u^z\)), the radial (axial) component of the velocity. As a by-product, weighted regularity condition via \(\omega ^{\theta }\) is also established. These extend previous results significantly.

Keywords

Axisymmetric Navier–Stokes equations regularity criteria negative weightes 

Mathematics Subject Classification

35B65 35Q35 76D03 

Notes

Acknowledgements

We are grateful to the anonymous reviewer for careful reading and suggestions which made the paper more readable. Zujin Zhang is partially supported by the National Natural Science Foundation of China (Grant No. 11761009).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceGannan Normal UniversityGanzhouPeople’s Republic of China

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