Displaying similar documents to “Weak solutions to the Navier-Stokes equations in a Y-shaped domain”

Time-dependent coupling of Navier–Stokes and Darcy flows

Aycil Cesmelioglu, Vivette Girault, Béatrice Rivière (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A weak solution of the coupling of time-dependent incompressible Navier–Stokes equations with Darcy equations is defined. The interface conditions include the Beavers–Joseph–Saffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces.

Lagrangian approximations and weak solutions of the Navier-Stokes equations

Werner Varnhorn (2008)

Banach Center Publications

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The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles...

Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system

Radim Hošek, Václav Mácha (2019)

Czechoslovak Mathematical Journal

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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...