Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn system
Analysis of PDEs
2017-11-15 v1
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 \emph{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.
Cite
@article{arxiv.1711.04488,
title = {Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn system},
author = {Radim Hošek and Václav Mácha},
journal= {arXiv preprint arXiv:1711.04488},
year = {2017}
}