Geodesic
A NEW REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS
YUE, HU1 ; LI, WU-MING1
1 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 2, p. 126-129.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We study the incompressible Navier-Stokes equations in the entire three-dimensional space. We prove that if $\partial_3u_3 \in L^{s_1}_ t L^{r_1}_x$ and $u_1u_2 \in L^{s_2}_ t L^{r_2}_x$, then the solution is regular. Here $\frac{2}{s_1}+\frac{3}{r_1}\leq 1, 3\leq r_1\leq\infty,\frac{2}{s_2}+\frac{3}{r_2}\leq1$ and $3\leq r_2\leq\infty$.
DOI : 10.22436/jnsa.004.02.04
Classification : 35Q30, 76D03
Keywords: Navier-Stokes equations, Leray-Hopf weak solution, Regularity.

YUE, HU 1 ; LI, WU-MING 1

1 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China 
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YUE, HU; LI, WU-MING. A NEW REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 2, p. 126-129. doi : 10.22436/jnsa.004.02.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.02.04/

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