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Existence of weak solutions for a Bingham fluid-rigid body system |
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| Affiliation: | 1. Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile;2. Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France;1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany;2. Department of Computational Science and Engineering, Yonsei University, Seoul, Republic of Korea;3. Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany;1. Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland;2. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland |
| 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. |
| Keywords: | Bingham fluid Rigid body Fluid-structure interaction systems Weak solutions |
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