Regularity criterion via the pressure on weak solutions to the 3D Navier-Stokes equations
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- by Chen Qionglei and Zhang Zhifei PDF
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Abstract:
We consider the regularity of weak solutions to the Navier-Stokes equations in $\mathbb {R}^3$. Let $u$ be a Leray-Hopf weak solution. It is proved that $u$ becomes a regular solution if the pressure $p \in L^1(0,T; \dot B^0_{\infty ,\infty })$.References
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Additional Information
- Chen Qionglei
- Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China
- Email: chen_qionglei@iapcm.ac.cn
- Zhang Zhifei
- Affiliation: School of Mathematical Science, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 703192
- Email: zfzhang@math.pku.edu.cn
- Received by editor(s): May 15, 2004
- Received by editor(s) in revised form: February 7, 2006
- Published electronically: December 29, 2006
- Additional Notes: The second author is supported by National Natural Science Foundation of China (10601002)
- Communicated by: David S. Tartakoff
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1829-1837
- MSC (2000): Primary 35Q30, 35B65, 76D03
- DOI: https://doi.org/10.1090/S0002-9939-06-08663-1
- MathSciNet review: 2286093