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Chinese Annals of Mathematics, Series B

, Volume 36, Issue 6, pp 947–956 | Cite as

On the Serrin’s regularity criterion for the β-generalized dissipative surface quasi-geostrophic equation

  • Jihong ZhaoEmail author
  • Qiao Liu
Article
  • 43 Downloads

Abstract

The authors establish a Serrin’s regularity criterion for the β-generalized dissipative surface quasi-geostrophic equation. More precisely, it is shown that if the smooth solution θ satisfies ∇θ ∈ L q (0, T;L q (R2)) with \(\frac{\alpha }{q} + \frac{2}{p} \leqslant \alpha + \beta - 1\), then the solution θ can be smoothly extended after time T. In particular, when α + β ≥ 2, it is shown that if ∂yθ ∈ L q (0, T;L q (R2)) with \(\frac{\alpha }{q} + \frac{2}{p} \leqslant \alpha + \beta - 1\), then the solution θ can also be smoothly extended after time T. This result extends the regularity result of Yamazaki in 2012.

Keywords

β-generalized quasi-geostrophic equation Weak solution Serrin’s regularity criterion 

2010 MR Subject Classification

35B65 35Q86 35R11 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.College of ScienceNorthwest A&F UniversityYangling, ShaanxiChina
  2. 2.Department of MathematicsHunan Normal UniversityChangshaChina

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