| Title:
|
Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system (English) |
| Author:
|
Hošek, Radim |
| Author:
|
Mácha, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
837-851 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Allen-Cahn system |
| Keyword:
|
weak-strong uniqueness |
| MSC:
|
35A02 |
| MSC:
|
35B65 |
| idZBL:
|
Zbl 07088819 |
| idMR:
|
MR3989281 |
| DOI:
|
10.21136/CMJ.2019.0520-17 |
| . |
| Date available:
|
2019-07-24T11:20:12Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147792 |
| . |
| Reference:
|
[1] Březina, J., Kreml, O., Mácha, V.: Dimension reduction for the full Navier-Stokes-Fourier system.J. Math. Fluid Mech. 19 (2017), 659-683. Zbl 1386.35335, MR 3714498, 10.1007/s00021-016-0301-6 |
| Reference:
|
[2] Dafermos, C. M.: The second law of thermodynamics and stability.Arch. Ration. Mech. Anal. 70 (1979), 167-179. Zbl 0448.73004, MR 0546634, 10.1007/BF00250353 |
| Reference:
|
[3] Ducomet, B., Nečasová, Š.: Diffusion limits in a model of radiative flow.Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 61 (2015), 17-59. Zbl 1331.35276, MR 3343442, 10.1007/s11565-014-0214-3 |
| Reference:
|
[4] Feireisl, E., Jin, B. J., Novotný, A.: Inviscid incompressible limits of strongly stratified fluids.Asymptotic Anal. 89 (2014), 307-329. Zbl 1304.35540, MR 3266143, 10.3233/ASY-141231 |
| Reference:
|
[5] Feireisl, E., Klein, R., Novotný, A., Zatorska, E.: On singular limits arising in the scale analysis of stratified fluid flows.Math. Models Methods Appl. Sci. 26 (2016), 419-443. Zbl 1339.35210, MR 3458246, 10.1142/S021820251650007X |
| Reference:
|
[6] Feireisl, E., Novotný, A.: Weak-strong uniqueness property for the full Navier-Stokes-Fourier system.Arch. Ration. Mech. Anal. 204 (2012), 683-706. Zbl 1285.76034, MR 2909912, 10.1007/s00205-011-0490-3 |
| Reference:
|
[7] Lin, F.-H., Liu, C.: Nonparabolic dissipative systems modeling the flow of liquid crystals.Commun. Pure Appl. Math. 48 (1995), 501-537. Zbl 0842.35084, MR 1329830, 10.1002/cpa.3160480503 |
| Reference:
|
[8] Sohr, H.: The Navier-Stokes Equations. An Elementary Functional Analytic Approach.Birkhäuser Advanced Texts, Birkhäuser, Basel (2001). Zbl 0983.35004, MR 1928881, 10.1007/978-3-0348-8255-2 |
| Reference:
|
[9] Zhao, L., Guo, B., Huang, H.: Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system.J. Math. Anal. Appl. 384 (2011), 232-245. Zbl 1231.35185, MR 2825177, 10.1016/j.jmaa.2011.05.042 |
| . |
