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

Obando, Benjamin; Takahashi, Takéo

Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 5, pp. 1281-1309.

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.

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