Local well-posedness for a two-phase model with magnetic field and vacuum

Xiuhui Yang

Applications of Mathematics (2021)

  • Volume: 66, Issue: 4, page 619-639
  • ISSN: 0862-7940

Abstract

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This paper proves the local well-posedness of strong solutions to a two-phase model with magnetic field and vacuum in a bounded domain Ω ⊂ ℝ 3 without the standard compatibility conditions.

How to cite

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Yang, Xiuhui. "Local well-posedness for a two-phase model with magnetic field and vacuum." Applications of Mathematics 66.4 (2021): 619-639. <http://eudml.org/doc/297455>.

@article{Yang2021,
abstract = {This paper proves the local well-posedness of strong solutions to a two-phase model with magnetic field and vacuum in a bounded domain $\Omega \subset \mathbb \{R\}^3$ without the standard compatibility conditions.},
author = {Yang, Xiuhui},
journal = {Applications of Mathematics},
keywords = {two-phase flow; magnetic field; vacuum; local well-posedness},
language = {eng},
number = {4},
pages = {619-639},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local well-posedness for a two-phase model with magnetic field and vacuum},
url = {http://eudml.org/doc/297455},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Yang, Xiuhui
TI - Local well-posedness for a two-phase model with magnetic field and vacuum
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 619
EP - 639
AB - This paper proves the local well-posedness of strong solutions to a two-phase model with magnetic field and vacuum in a bounded domain $\Omega \subset \mathbb {R}^3$ without the standard compatibility conditions.
LA - eng
KW - two-phase flow; magnetic field; vacuum; local well-posedness
UR - http://eudml.org/doc/297455
ER -

References

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  1. Berselli, L. C., Spirito, S., 10.1007/s00220-012-1581-1, Commun. Math. Phys. 316 (2012), 171-198. (2012) Zbl1254.35175MR2989457DOI10.1007/s00220-012-1581-1
  2. Carrillo, J. A., Goudon, T., 10.1080/03605300500394389, Commun. Partial Differ. Equations 31 (2006), 1349-1379. (2006) Zbl1105.35088MR2254618DOI10.1080/03605300500394389
  3. Cho, Y., Choe, H. J., Kim, H., 10.1016/j.matpur.2003.11.004, J. Math. Pures Appl., IX. Sér. 83 (2004), 243-275. (2004) Zbl1080.35066MR2038120DOI10.1016/j.matpur.2003.11.004
  4. Choe, H. J., Kim, H., 10.1016/S0022-0396(03)00015-9, J. Differ. Equations 190 (2003), 504-523. (2003) Zbl1022.35037MR1970039DOI10.1016/S0022-0396(03)00015-9
  5. Enomoto, Y., Shibata, Y., 10.1619/fesi.56.441, Funkc. Ekvacioj, Ser. Int. 56 (2013), 441-505. (2013) Zbl1296.35118MR3157151DOI10.1619/fesi.56.441
  6. Fan, J., Yu, W., 10.1016/j.nonrwa.2007.10.001, Nonlinear Anal., Real World Appl. 10 (2009), 392-409. (2009) Zbl1154.76389MR2451719DOI10.1016/j.nonrwa.2007.10.001
  7. Gong, H., Li, J., Liu, X.-G., Zhang, X., 10.4310/CMS.2020.v18.n7.a4, Commun. Math. Sci. 18 (2020), 1891-1909. (2020) Zbl07342276MR4195559DOI10.4310/CMS.2020.v18.n7.a4
  8. Hong, G., Hou, X., Peng, H., Zhu, C., 10.1137/16M1100447, SIAM J. Math. Anal. 49 (2017), 2409-2441. (2017) Zbl1372.35164MR3668595DOI10.1137/16M1100447
  9. Huang, X., 10.1007/s11425-019-9755-3, (to appear) in Sci. China, Math. DOI10.1007/s11425-019-9755-3
  10. Métivier, G., Schochet, S., 10.1007/PL00004241, Arch. Ration. Mech. Anal. 158 (2001), 61-90. (2001) Zbl0974.76072MR1834114DOI10.1007/PL00004241
  11. Nowakowski, B., Ströhmer, G., Zajączkowski, W. M., 10.1007/s00021-017-0353-2, J. Math. Fluid Mech. 20 (2018), 1013-1034. (2018) Zbl1401.35253MR3841971DOI10.1007/s00021-017-0353-2
  12. Nowakowski, B., Zajączkowski, W. M., 10.1007/s00033-016-0734-z, Z. Angew. Math. Phys. 67 (2016), Article ID 142, 22 pages. (2016) Zbl1358.35128MR3566925DOI10.1007/s00033-016-0734-z
  13. Piasecki, T., Shibata, Y., Zatorska, E., 10.1137/17M1151134, SIAM J. Math. Anal. 51 (2019), 2793-2849. (2019) Zbl1419.76541MR3977107DOI10.1137/17M1151134
  14. Vasseur, A., Wen, H., Yu, C., 10.1016/j.matpur.2018.06.019, J. Math. Pures Appl. (9) 125 (2019), 247-282. (2019) Zbl1450.76033MR3944205DOI10.1016/j.matpur.2018.06.019
  15. Wen, H., Zhu, L., 10.1016/j.jde.2017.10.027, J. Differ. Equations 264 (2018), 2377-2406. (2018) Zbl1432.76298MR3721432DOI10.1016/j.jde.2017.10.027
  16. Zhu, S., 10.1137/14095265X, SIAM J. Math. Anal. 47 (2015), 2722-2753. (2015) Zbl1325.35176MR3369066DOI10.1137/14095265X

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