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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.
Keywords:  Allen-Cahn system; weak-strong uniqueness
Classification MSC:  35A02, 35B65
DOI:  10.21136/CMJ.2019.0520-17
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Affiliations:   Radim Hošek, Václav Mácha, Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail: hosek@math.cas.cz, macha@math.cas.cz
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