On the Navier–Stokes system with the Coulomb friction law boundary condition

Abstract : We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier–Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two–dimensional problem and the existence of at least one solution in the three–dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method and we present numerical simulations in two physical examples.
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Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2017
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Loredana Bălilescu, Jorge San Martín, Takéo Takahashi. On the Navier–Stokes system with the Coulomb friction law boundary condition. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2017. <hal-01393709>

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