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

Zujin Zhang

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

机译：涉及一种速度和一种涡度分量的Navier-Stokes方程的Serrin型正则性准则

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摘要

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. Pokorny (2004).

机译：我们考虑了三维Navier-Stokes方程的Cauchy问题，并根据$ u_3 $和$ omega_3 $提供了最优的正则性判据，它们分别是速度和涡度的第三个分量。这为P.Penel，M.Pokorny（2004）的论文中的一个开放性问题提供了肯定的答案。

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《Czechoslovak Mathematical Journal》 |2018年第1期|共7页
作者
Zujin Zhang;
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中图分类数学;
关键词
regularity criterionNavier-Stokes equation;

机译：正则性准则Navier-Stokes方程;

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专利

1. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component [J] . Zhang Zujin Czechoslovak Mathematical Journal . 2018,第1期

机译：涉及一个速度和一个涡旋组件的Navier-Stokes方程的Serrin型规律标准
2. An almost Serrin-type regularity criterion for the Navier-Stokes equations involving the gradient of one velocity component [J] . Zhang Zujin ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2015,第4期

机译：涉及一个速度分量梯度的Navier-Stokes方程的近似Serrin型正则性准则
3. A regularity criterion of Serrin-type for the Navier-Stokes equations involving the gradient of one velocity component [J] . Joerg Wolf Analysis . 2015,第4期

机译：涉及一个速度分量梯度的Navier-Stokes方程的Serrin型正则性判据
4. On the Divergence-Free Condition of Velocity and Vorticity in Velocity-Vorticity Formulation of Incompressible Navier-Stokes Equation [C] . Swagata Bhaumik, Tapan K. Sengupta AIAA computational fluid dynamics conference . 2011

机译：关于不可压缩的Navier-Stokes方程的速度-涡度公式化中的速度和涡度的无散度条件
5. On elliptic equations with low-regularity divergence-free drift terms and the steady-state Navier-Stokes equations in higher dimensions. [D] . Kontovourkis, Michalis. 2007

机译：具有低规则性无散度漂移项的椭圆方程和高维稳态Navier-Stokes方程。
6. An Osgood Type Regularity Criterion for the 3D Boussinesq Equations [O] . Qiang Wu, Lin Hu, Guili Liu -1

机译：3D Boussinesq方程的Osgood类型正则性准则
7. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component [O] . Zujin Zhang 2017

机译：涉及一个速度和一个涡旋组件的Navier-Stokes方程的Serrin型规律标准

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

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