Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
Czechoslovak Mathematical Journal (2019)
- Volume: 69, Issue: 3, page 837-851
- ISSN: 0011-4642
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topHošek, Radim, and Mácha, Václav. "Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system." Czechoslovak Mathematical Journal 69.3 (2019): 837-851. <http://eudml.org/doc/294873>.
@article{Hošek2019,
abstract = {The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative entropy method.},
author = {Hošek, Radim, Mácha, Václav},
journal = {Czechoslovak Mathematical Journal},
keywords = {Allen-Cahn system; weak-strong uniqueness},
language = {eng},
number = {3},
pages = {837-851},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system},
url = {http://eudml.org/doc/294873},
volume = {69},
year = {2019},
}
TY - JOUR
AU - Hošek, Radim
AU - Mácha, Václav
TI - Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 837
EP - 851
AB - The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative entropy method.
LA - eng
KW - Allen-Cahn system; weak-strong uniqueness
UR - http://eudml.org/doc/294873
ER -
References
top- Březina, J., Kreml, O., Mácha, V., 10.1007/s00021-016-0301-6, J. Math. Fluid Mech. 19 (2017), 659-683. (2017) Zbl1386.35335MR3714498DOI10.1007/s00021-016-0301-6
- Dafermos, C. M., 10.1007/BF00250353, Arch. Ration. Mech. Anal. 70 (1979), 167-179. (1979) Zbl0448.73004MR0546634DOI10.1007/BF00250353
- Ducomet, B., Nečasová, Š., 10.1007/s11565-014-0214-3, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 61 (2015), 17-59. (2015) Zbl1331.35276MR3343442DOI10.1007/s11565-014-0214-3
- Feireisl, E., Jin, B. J., Novotný, A., 10.3233/ASY-141231, Asymptotic Anal. 89 (2014), 307-329. (2014) Zbl1304.35540MR3266143DOI10.3233/ASY-141231
- Feireisl, E., Klein, R., Novotný, A., Zatorska, E., 10.1142/S021820251650007X, Math. Models Methods Appl. Sci. 26 (2016), 419-443. (2016) Zbl1339.35210MR3458246DOI10.1142/S021820251650007X
- Feireisl, E., Novotný, A., 10.1007/s00205-011-0490-3, Arch. Ration. Mech. Anal. 204 (2012), 683-706. (2012) Zbl1285.76034MR2909912DOI10.1007/s00205-011-0490-3
- Lin, F.-H., Liu, C., 10.1002/cpa.3160480503, Commun. Pure Appl. Math. 48 (1995), 501-537. (1995) Zbl0842.35084MR1329830DOI10.1002/cpa.3160480503
- Sohr, H., 10.1007/978-3-0348-8255-2, Birkhäuser Advanced Texts, Birkhäuser, Basel (2001). (2001) Zbl0983.35004MR1928881DOI10.1007/978-3-0348-8255-2
- Zhao, L., Guo, B., Huang, H., 10.1016/j.jmaa.2011.05.042, J. Math. Anal. Appl. 384 (2011), 232-245. (2011) Zbl1231.35185MR2825177DOI10.1016/j.jmaa.2011.05.042
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