An improved regularity criteria for the MHD system based on two components of the solution

Zujin Zhang; Yali Zhang

Applications of Mathematics (2021)

  • Volume: 66, Issue: 3, page 451-460
  • ISSN: 0862-7940

Abstract

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As observed by Yamazaki, the third component b 3 of the magnetic field can be estimated by the corresponding component u 3 of the velocity field in L λ ( 2 ≤ λ ≤ 6 ) norm. This leads him to establish regularity criterion involving u 3 , j 3 or u 3 , ω 3 . Noticing that λ can be greater than 6 in this paper, we can improve previous results.

How to cite

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Zhang, Zujin, and Zhang, Yali. "An improved regularity criteria for the MHD system based on two components of the solution." Applications of Mathematics 66.3 (2021): 451-460. <http://eudml.org/doc/297790>.

@article{Zhang2021,
abstract = {As observed by Yamazaki, the third component $b_3$ of the magnetic field can be estimated by the corresponding component $u_3$ of the velocity field in $L^\{\lambda \}$$(2\le \lambda \le 6)$ norm. This leads him to establish regularity criterion involving $u_3, j_3$ or $u_3,\omega _3$. Noticing that $\lambda $ can be greater than 6 in this paper, we can improve previous results.},
author = {Zhang, Zujin, Zhang, Yali},
journal = {Applications of Mathematics},
keywords = {MHD equations; regularity criteria},
language = {eng},
number = {3},
pages = {451-460},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An improved regularity criteria for the MHD system based on two components of the solution},
url = {http://eudml.org/doc/297790},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Zhang, Zujin
AU - Zhang, Yali
TI - An improved regularity criteria for the MHD system based on two components of the solution
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 451
EP - 460
AB - As observed by Yamazaki, the third component $b_3$ of the magnetic field can be estimated by the corresponding component $u_3$ of the velocity field in $L^{\lambda }$$(2\le \lambda \le 6)$ norm. This leads him to establish regularity criterion involving $u_3, j_3$ or $u_3,\omega _3$. Noticing that $\lambda $ can be greater than 6 in this paper, we can improve previous results.
LA - eng
KW - MHD equations; regularity criteria
UR - http://eudml.org/doc/297790
ER -

References

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  1. Cao, C., Wu, J., 10.1016/j.jde.2009.09.020, J. Differ. Equations 248 (2010), 2263-2274. (2010) Zbl1190.35046MR2595721DOI10.1016/j.jde.2009.09.020
  2. Chemin, J.-Y., Zhang, P., 10.24033/asens.2278, Ann. Sci. Éc. Norm. Supér. 49 (2016), 131-167. (2016) Zbl1342.35210MR3465978DOI10.24033/asens.2278
  3. Chen, Q., Miao, C., Zhang, Z., 10.1007/s00220-008-0545-y, Commun. Math. Phys. 284 (2008), 919-930. (2008) Zbl1168.35035MR2452599DOI10.1007/s00220-008-0545-y
  4. Duan, H., 10.1080/00036811.2011.556626, Appl. Anal. 91 (2012), 947-952. (2012) Zbl1247.35101MR2911243DOI10.1080/00036811.2011.556626
  5. Duvaut, G., Lions, J. L., 10.1007/BF00250512, Arch. Ration. Mech. Anal. 46 (1972), 241-279 French. (1972) Zbl0264.73027MR0346289DOI10.1007/BF00250512
  6. He, C., Xin, Z., 10.1016/j.jde.2004.07.002, J. Differ. Equations 213 (2005), 235-254. (2005) Zbl1072.35154MR2142366DOI10.1016/j.jde.2004.07.002
  7. Ji, E., Lee, J., 10.1016/j.jmaa.2010.03.015, J. Math. Anal. Appl. 369 (2010), 317-322. (2010) Zbl1196.35063MR2643871DOI10.1016/j.jmaa.2010.03.015
  8. Jia, X., 10.1016/j.aml.2015.05.017, Appl. Math. Lett. 50 (2015), 1-4. (2015) Zbl1327.35320MR3378940DOI10.1016/j.aml.2015.05.017
  9. Jia, X., Zhou, Y., 10.1016/j.nonrwa.2011.07.055, Nonlinear Anal., Real World Appl. 13 (2012), 410-418. (2012) Zbl1239.35032MR2846851DOI10.1016/j.nonrwa.2011.07.055
  10. Jia, X., Zhou, Y., 10.1088/0951-7715/28/9/3289, Nonlinearity 28 (2015), 3289-3307. (2015) Zbl1326.35276MR3403399DOI10.1088/0951-7715/28/9/3289
  11. Jia, X., Zhou, Y., 10.1007/s00021-015-0246-1, J. Math. Fluid Mech. 18 (2016), 187-206. (2016) Zbl1334.35240MR3461931DOI10.1007/s00021-015-0246-1
  12. Ni, L., Guo, Z., Zhou, Y., 10.1016/j.jmaa.2012.05.076, J. Math. Anal. Appl. 396 (2012), 108-118. (2012) Zbl1247.35095MR2956948DOI10.1016/j.jmaa.2012.05.076
  13. Penel, P., Pokorný, M., 10.1007/s00021-010-0038-6, J. Math. Fluid Mech. 13 (2011), 341-353. (2011) Zbl1270.35354MR2824487DOI10.1007/s00021-010-0038-6
  14. Sermange, M., Temam, R., 10.1002/cpa.3160360506, Commun. Pure Appl. Math. 36 (1983), 635-664. (1983) Zbl0524.76099MR0716200DOI10.1002/cpa.3160360506
  15. Yamazaki, K., 10.1007/s00021-014-0178-1, J. Math. Fluid Mech. 16 (2014), 551-570. (2014) Zbl1307.35237MR3247368DOI10.1007/s00021-014-0178-1
  16. Yamazaki, K., 10.1063/1.4868277, J. Math. Phys. 55 (2014), Article ID 031505, 16 pages. (2014) Zbl1286.76172MR3221239DOI10.1063/1.4868277
  17. Yamazaki, K., 10.1016/j.bulsci.2015.08.003, Bull. Sci. Math. 140 (2016), 575-614. (2016) Zbl1345.35081MR3509263DOI10.1016/j.bulsci.2015.08.003
  18. Yamazaki, K., 10.1016/j.na.2016.01.015, Nonlinear Anal., Theory Methods Appl., Ser. A 135 (2016), 73-83. (2016) Zbl1345.35080MR3473110DOI10.1016/j.na.2016.01.015
  19. Yamazaki, K., Horizontal Biot-Savart law in general dimension and an application to the 4D magneto-hydrodynamics, Differ. Integral Equ. 31 (2018), 301-328. (2018) Zbl06837099MR3738200
  20. Zhang, Z., 10.1016/j.na.2014.12.003, Nonlinear Anal., Theory Methods Appl., Ser. A 115 (2015), 41-49. (2015) Zbl1309.35095MR3305136DOI10.1016/j.na.2014.12.003
  21. Zhang, Z., 10.1007/s00033-014-0461-2, Z. Angew. Math. Phys. 66 (2015), 977-987. (2015) Zbl1329.35097MR3347420DOI10.1007/s00033-014-0461-2
  22. Zhang, Z., 10.1080/00036811.2016.1207245, Appl. Anal. 96 (2017), 2130-2139. (2017) Zbl1372.35064MR3667850DOI10.1080/00036811.2016.1207245
  23. Zhang, Z., Yao, Z.-a., Lu, M., Ni, L., 10.1063/1.3589966, J. Math. Phys. 52 (2011), Article ID 053103, 7 pages. (2011) Zbl1317.35180MR2839081DOI10.1063/1.3589966
  24. Zhou, Y., 10.3934/dcds.2005.12.881, Discrete Contin. Dyn. Syst. 12 (2005), 881-886. (2005) Zbl1068.35117MR2128731DOI10.3934/dcds.2005.12.881
  25. Zhou, Y., Fan, J., 10.1515/form.2011.079, Forum Math. 24 (2012), 691-708. (2012) Zbl1247.35115MR2949119DOI10.1515/form.2011.079

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