Geodesic
Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 837-851
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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.
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.
DOI : 10.21136/CMJ.2019.0520-17
Classification : 35A02, 35B65
Keywords: Allen-Cahn system; weak-strong uniqueness 
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Hošek, Radim; Mácha, Václav. Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 837-851. doi: 10.21136/CMJ.2019.0520-17

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