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

Loredana Bălilescu (1, 2) , Jorge San Martín (3, 4) , Takéo Takahashi (5, 6)

1 MTM - Departamento de Matemática = Mathematics Department [Florianópolis]
2 Department of Mathematics [Pitesti]
3 CMM - Center for Mathematical Modeling
4 DIM - Departamento de Ingeniería Matemática [Santiago]
5 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
6 IECL - Institut Élie Cartan de Lorraine

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.

Domaines: Equations aux dérivées partielles [math.AP]

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, 2017, 68 (3), ⟨10.1007/s00033-016-0744-x⟩. ⟨hal-01393709⟩