On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1165-1175 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.
This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.
DOI : 10.21136/CMJ.2019.0128-18
Classification : 35B65, 35Q30, 76D03
Keywords: regularity criteria; Navier-Stokes equations
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     title = {On ratio improvement of {Prodi-Serrin-Ladyzhenskaya} type regularity criteria for the {Navier-Stokes} system},
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Zhang, Zujin; Wu, Chupeng; Zhou, Yong. On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1165-1175. doi: 10.21136/CMJ.2019.0128-18

[1] Veiga, H. Beirão da: A new regularity class for the Navier-Stokes equations in $\mathbb{R}^n$. Chin. Ann. Math., Ser. B 16 (1995), 407-412. | MR | JFM

[2] Constantin, P., Fefferman, C.: Direction of vorticity and the problem of global regularity for the Navier-Stokes equations. Indiana Univ. Math. J. 42 (1993), 775-789. | DOI | MR | JFM

[3] Escauriaza, L., Serëgin, G. A., Shverak, V.: $L_{3,\infty}$-solutions of Navier-Stokes equations and backward uniqueness. Russ. Math. Surv. 58 (2003), 211-250 translation from Usp. Mat. Nauk 58 2003 3-44. | DOI | MR | JFM

[4] Fujita, H., Kato, T.: On the Navier-Stokes initial value problem. I. Arch. Ration. Mech. Anal. 16 (1964), 269-315. | DOI | MR | JFM

[5] Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951), 213-321 German. | DOI | MR | JFM

[6] Kato, T.: Strong $L^p$-solutions of the Navier-Stokes equation in $\mathbb{R}^m$, with applications to weak solutions. Math. Z. 187 (1984), 471-480. | DOI | MR | JFM

[7] Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934), 193-248 French \99999JFM99999 60.0726.05. | DOI | MR

[8] Prodi, G.: Un teorema di unicità per le equazioni di Navier-Stokes. Ann. Mat. Pura Appl., IV. Ser. 48 (1959), 173-182 Italian. | DOI | MR | JFM

[9] Robinson, J. C., Rodrigo, J. L., Sadowski, W.: The Three-Dimensional Navier-Stokes Equations. Classical Theory. Cambridge Studies in Advanced Mathematics 157, Cambridge University Press, Cambridge (2016). | DOI | MR | JFM

[10] Schoen, R., Yau, S.-T.: Lectures on Differential Geometry. Conference Proceedings and Lecture Notes in Geometry and Topology 1, International Press, Cambridge (1994). | MR | JFM

[11] Serrin, J.: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 9 (1962), 187-195. | DOI | MR | JFM

[12] Sohr, H., Wahl, W. von: On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscr. Math. 49 (1984), 27-59. | DOI | MR | JFM

[13] Tran, C. V., Yu, X.: Depletion of nonlinearity in the pressure force driving Navier-Stokes flows. Nonlinearity 28 (2015), 1295-1306. | DOI | MR | JFM

[14] Tran, C. V., Yu, X.: Pressure moderation and effective pressure in Navier-Stokes flows. Nonlinearity 29 (2016), 2290-3005. | DOI | MR | JFM

[15] Tran, C. V., Yu, X.: Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations. J. Math. Phys. 58 (2017), 011501, 10 pages. | DOI | MR | JFM

[16] Vasseur, A.: Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity. Appl. Math., Praha 54 (2009), 47-52. | DOI | MR | JFM

[17] Zhang, Z., Yang, X.: Navier-Stokes equations with vorticity in Besov spaces of negative regular indices. J. Math. Anal. Appl. 440 (2016), 415-419. | DOI | MR | JFM

[18] Zhang, Z., Zhou, Y.: On regularity criteria for the 3D Navier-Stokes equations involving the ratio of the vorticity and the velocity. Comput. Math. Appl. 72 (2016), 2311-2314. | DOI | MR | JFM

[19] Zhou, Y.: Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain. Math. Ann. 328 (2004), 173-192. | DOI | MR | JFM

[20] Zhou, Y.: A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity. Monatsh. Math. 144 (2005), 251-257. | DOI | MR | JFM

[21] Zhou, Y.: Direction of vorticity and a new regularity criterion for the Navier-Stokes equations. ANZIAM J. 46 (2005), 309-316. | DOI | MR | JFM

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