Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system

Nana Pan; Jishan Fan; Yong Zhou

Applications of Mathematics (2021)

  • Volume: 66, Issue: 3, page 373-382
  • ISSN: 0862-7940

Abstract

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We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in ℝ 3 . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.

How to cite

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Pan, Nana, Fan, Jishan, and Zhou, Yong. "Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system." Applications of Mathematics 66.3 (2021): 373-382. <http://eudml.org/doc/297584>.

@article{Pan2021,
abstract = {We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in $\mathbb \{R\}^3$. It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.},
author = {Pan, Nana, Fan, Jishan, Zhou, Yong},
journal = {Applications of Mathematics},
keywords = {Ginzburg-Landau; Navier-Stokes; regularity criterion},
language = {eng},
number = {3},
pages = {373-382},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system},
url = {http://eudml.org/doc/297584},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Pan, Nana
AU - Fan, Jishan
AU - Zhou, Yong
TI - Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 373
EP - 382
AB - We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in $\mathbb {R}^3$. It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.
LA - eng
KW - Ginzburg-Landau; Navier-Stokes; regularity criterion
UR - http://eudml.org/doc/297584
ER -

References

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  1. Akiyama, T., Kasai, H., Tsutsumi, M., On the existence of the solution of the time dependent Ginzburg-Landau equations in ℝ 3 , Funkc. Ekvacioj., Ser. Int. 43 (2000), 255-270. (2000) Zbl1142.35561MR1795973
  2. Chen, J., Elliott, C. M., Qi, T., 10.1051/m2an/1998320100251, RAIRO, Modélisation Math. Anal. Numér. 32 (1998), 25-50. (1998) Zbl0905.35084MR1619592DOI10.1051/m2an/1998320100251
  3. Choe, H. J., Kim, H., 10.1081/PDE-120021191, Commun. Partial Differ. Equations 28 (2003), 1183-1201. (2003) Zbl1024.76010MR1986066DOI10.1081/PDE-120021191
  4. Fan, J., Gao, H., Guo, B., 10.1093/imrn/rnt253, Int. Math. Res. Not. 2015 (2015), 1239-1246. (2015) Zbl1317.35248MR3340353DOI10.1093/imrn/rnt253
  5. Fan, J., Jiang, S., 10.1016/S0893-9659(03)80069-1, Appl. Math. Lett. 16 (2003), 435-440. (2003) Zbl1055.35109MR1961437DOI10.1016/S0893-9659(03)80069-1
  6. Fan, J., Jing, L., Nakamura, G., Tang, T., 10.4064/ap190616-15-4, Ann. Pol. Math. 125 (2020), 47-57. (2020) Zbl07233404MR4121379DOI10.4064/ap190616-15-4
  7. Fan, J., Ozawa, T., 10.1088/0951-7715/22/3/003, Nonlinearity 22 (2009), 553-568. (2009) Zbl1168.35416MR2480102DOI10.1088/0951-7715/22/3/003
  8. Fan, J., Ozawa, T., 10.11650/tjm/180102, Taiwanese J. Math. 22 (2018), 851-858. (2018) Zbl1404.35425MR3830823DOI10.11650/tjm/180102
  9. Fan, J., Samet, B., Zhou, Y., 10.1016/j.camwa.2018.01.044, Comput. Math. Appl. 75 (2018), 3244-3248. (2018) Zbl1409.82022MR3785556DOI10.1016/j.camwa.2018.01.044
  10. Fan, J., Zhang, Z., Zhou, Y., 10.1007/s40840-019-00866-x, Bull. Malays. Math. Sci. Soc. (2) 43 (2020), 1009-1024. (2020) Zbl07173803MR4044915DOI10.1007/s40840-019-00866-x
  11. Fan, J., Zhou, Y., 10.1016/j.aml.2020.106208, Appl. Math. Lett. 103 (2020), Article ID 106208, 7 pages. (2020) Zbl07208182MR4050827DOI10.1016/j.aml.2020.106208
  12. Fan, J., Zhou, Y., 10.1016/j.jmaa.2019.123653, J. Math. Anal. Appl. 483 (2020), Article ID 123653, 7 pages. (2020) Zbl07153756MR4037584DOI10.1016/j.jmaa.2019.123653
  13. Hou, Q., Xu, X., Ye, Z., Logarithmically improved blow-up criteria for the 3D nonhomogeneous incompressible Navier-Stokes equations with vacuum, Electron. J. Differ. Equ. 2016 (2016), Article ID 192, 12 pages. (2016) Zbl1344.35080MR3547381
  14. Kim, H., 10.1137/S0036141004442197, SIAM J. Math. Anal. 37 (2006), 1417-1434. (2006) Zbl1141.35432MR2215270DOI10.1137/S0036141004442197
  15. Kozono, H., Shimada, Y., 10.1002/mana.200310213, Math. Nachr. 276 (2004), 63-74. (2004) Zbl1078.35087MR2100048DOI10.1002/mana.200310213
  16. Tang, Q., 10.1080/03605309508821085, Commun. Partial Differ. Equations 20 (1995), 1-36. (1995) Zbl0833.35132MR1312698DOI10.1080/03605309508821085
  17. Tang, Q., Wang, S., 10.1016/0167-2789(95)00195-A, Physica D 88 (1995), 139-166. (1995) Zbl0900.35371MR1360881DOI10.1016/0167-2789(95)00195-A

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