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arXiv · 1711.04488

Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn system

Radim Hošek·Václav Mácha
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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.

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Radim Hošek, Václav Mácha. 2017-11-13. Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn system. https://arxiv.org/abs/1711.04488

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