Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component

Zujin Zhang

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 219-225
  • ISSN: 0011-4642

Abstract

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We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of u 3 and ω 3 , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).

How to cite

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Zhang, Zujin. "Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component." Czechoslovak Mathematical Journal 68.1 (2018): 219-225. <http://eudml.org/doc/294242>.

@article{Zhang2018,
abstract = {We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of $u_3$ and $\omega _3$, which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).},
author = {Zhang, Zujin},
journal = {Czechoslovak Mathematical Journal},
keywords = {regularity criterion; Navier-Stokes equation},
language = {eng},
number = {1},
pages = {219-225},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component},
url = {http://eudml.org/doc/294242},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Zhang, Zujin
TI - Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 219
EP - 225
AB - We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of $u_3$ and $\omega _3$, which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).
LA - eng
KW - regularity criterion; Navier-Stokes equation
UR - http://eudml.org/doc/294242
ER -

References

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