Radim Hošek, Václav Mácha
Published 2017-11-13Version 1
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.
Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems
Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in ${\mathbb R}^3$
Navier-Stokes equations in a curved thin domain, Part II: global existence of a strong solution
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