Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system

Radim Hošek; Václav Mácha

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 3, page 837-851
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Hošek, 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

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