Fluid-rigid structure interaction system with Coulomb's law

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

1 Department of Mathematics [Pitesti]
2 MTM - Departamento de Matemática = Mathematics Department [Florianópolis]
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 in a fluid-structure system composed by a rigid body and a viscous incompress-ible fluid using a boundary condition based on Coulomb's law. This boundary condition allows the fluid to slip on the boundary if the tangential component of the stress is too large. In the opposite case, we recover the standard Dirichlet boundary condition. The governing equations are the Navier-Stokes system for the fluid and the Newton laws for the body. The corresponding coupled system can be written as a variational inequality. We prove that there exists a weak solution of this system.

Mots clés: Navier-Stokes system; Cauchy theory; Fluid-structure system; Coulomb's law 2010 Mathematics Subject Classification: 35Q30; 76D03; 76D27

Domaines: Equations aux dérivées partielles [math.AP]

Loredana Bălilescu, Jorge San Martín, Takéo Takahashi. Fluid-rigid structure interaction system with Coulomb's law. SIAM Journal on Mathematical Analysis, 2017, 49 (6), pp.4625-4657. ⟨10.1137/16M1099947⟩. ⟨hal-01386574⟩