JournalsaihpcVol. 36, No. 5pp. 1281–1309

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

  • Benjamin Obando

    Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile, Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France

  • Takéo Takahashi

    Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
Existence of weak solutions for a Bingham fluid-rigid body system cover

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Abstract

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.

Cite this article

Benjamin Obando, Takéo Takahashi, Existence of weak solutions for a Bingham fluid-rigid body system. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 5, pp. 1281–1309

DOI 10.1016/J.ANIHPC.2018.12.001