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

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 inequal...

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Bibliographic Details
Published inAnnales de l'Institut Henri Poincaré. Analyse non linéaire Vol. 36; no. 5; pp. 1281 - 1309
Main Authors Obando, Benjamin, Takahashi, Takéo
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.08.2019
EMS
Subjects
Analysis of PDEs
Bingham fluid
Fluid-structure interaction systems
Mathematics
Rigid body
Weak solutions
Rigid body
Weak solutions
35Q35
Fluid-structure interaction systems
74F10
76D03
Bingham fluid
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Summary: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.
ISSN:0294-1449
1873-1430
DOI:10.1016/j.anihpc.2018.12.001