| Title:
|
On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system (English) |
| Author:
|
Zhang, Zujin |
| Author:
|
Wu, Chupeng |
| Author:
|
Zhou, Yong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
1165-1175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
regularity criteria |
| Keyword:
|
Navier-Stokes equations |
| MSC:
|
35B65 |
| MSC:
|
35Q30 |
| MSC:
|
76D03 |
| idZBL:
|
07144883 |
| idMR:
|
MR4039628 |
| DOI:
|
10.21136/CMJ.2019.0128-18 |
| . |
| Date available:
|
2019-11-28T08:54:30Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147922 |
| . |
| Reference:
|
[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. Zbl 0837.35111, MR 1380578 |
| Reference:
|
[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. Zbl 0837.35113, MR 1254117, 10.1512/iumj.1993.42.42034 |
| Reference:
|
[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. Zbl 1064.35134, MR 1992563, 10.1070/rm2003v058n02abeh000609 |
| Reference:
|
[4] Fujita, H., Kato, T.: On the Navier-Stokes initial value problem. I.Arch. Ration. Mech. Anal. 16 (1964), 269-315. Zbl 0126.42301, MR 0166499, 10.1007/bf00276188 |
| Reference:
|
[5] Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen.Math. Nachr. 4 (1951), 213-321 German. Zbl 0042.10604, MR 0050423, 10.1002/mana.3210040121 |
| Reference:
|
[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. Zbl 0545.35073, MR 0760047, 10.1007/bf01174182 |
| Reference:
|
[7] Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace.Acta Math. 63 (1934), 193-248 French \99999JFM99999 60.0726.05. MR 1555394, 10.1007/bf02547354 |
| Reference:
|
[8] Prodi, G.: Un teorema di unicità per le equazioni di Navier-Stokes.Ann. Mat. Pura Appl., IV. Ser. 48 (1959), 173-182 Italian. Zbl 0148.08202, MR 0126088, 10.1007/bf02410664 |
| Reference:
|
[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). Zbl 1358.35002, MR 3616490, 10.1017/cbo9781139095143 |
| Reference:
|
[10] Schoen, R., Yau, S.-T.: Lectures on Differential Geometry.Conference Proceedings and Lecture Notes in Geometry and Topology 1, International Press, Cambridge (1994). Zbl 0830.53001, MR 1333601 |
| Reference:
|
[11] Serrin, J.: On the interior regularity of weak solutions of the Navier-Stokes equations.Arch. Ration. Mech. Anal. 9 (1962), 187-195. Zbl 0106.18302, MR 0136885, 10.1007/bf00253344 |
| Reference:
|
[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. Zbl 0567.35069, MR 0762786, 10.1007/bf01174870 |
| Reference:
|
[13] Tran, C. V., Yu, X.: Depletion of nonlinearity in the pressure force driving Navier-Stokes flows.Nonlinearity 28 (2015), 1295-1306. Zbl 1312.76013, MR 3346162, 10.1088/0951-7715/28/5/1295 |
| Reference:
|
[14] Tran, C. V., Yu, X.: Pressure moderation and effective pressure in Navier-Stokes flows.Nonlinearity 29 (2016), 2290-3005. Zbl 1349.76046, MR 3551051, 10.1088/0951-7715/29/10/2990 |
| Reference:
|
[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. Zbl 1355.76017, MR 3597368, 10.1063/1.4974020 |
| Reference:
|
[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. Zbl 1212.35354, MR 2476020, 10.1007/s10492-009-0003-y |
| Reference:
|
[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. Zbl 1339.35221, MR 3479607, 10.1016/j.jmaa.2016.03.037 |
| Reference:
|
[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. Zbl 1372.35220, MR 3564413, 10.1016/j.camwa.2016.08.031 |
| Reference:
|
[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. Zbl 1054.35062, MR 2030374, 10.1007/s00208-003-0478-x |
| Reference:
|
[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. Zbl 1072.35148, MR 2130277, 10.1007/s00605-004-0266-z |
| Reference:
|
[21] Zhou, Y.: Direction of vorticity and a new regularity criterion for the Navier-Stokes equations.ANZIAM J. 46 (2005), 309-316. Zbl 1072.35565, MR 2124925, 10.1017/s1446181100008270 |
| . |
