Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 837-851, 2019
Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
Radim Hošek, Václav Mácha
Received November 13, 2017. Published online February 27, 2019.
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.