Existence of weak solutions for a Bingham fluid-rigid body system

Benjamin Obando (1, 2) , Takéo Takahashi (2, 3)

1 DIM - Departamento de Ingeniería Matemática [Santiago]
2 IECL - Institut Élie Cartan de Lorraine
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

We consider the motion of a rigid body in a viscoplastic material. This material is modeled by the 3D Bingham equations, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is an inequality (due to the plasticity of the fluid), and it involves a free boundary (due to the motion of the rigid body). We approximate it by regularizing the convex terms in the Bingham fluid and by using a penalty method to take into account the presence of the rigid body.

Domaines: Equations aux dérivées partielles [math.AP]

Benjamin Obando, Takéo Takahashi. Existence of weak solutions for a Bingham fluid-rigid body system. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019, 36 (5), pp.1281-1309. ⟨10.1016/j.anihpc.2018.12.001⟩. ⟨hal-01942426⟩