Comptes Rendus
no. 3
Analyse mathématique, Équations différentielles
On the 2D “viscous incompressible fluid + rigid body” system with Navier conditions and unbounded energy
[Sur le mouvement d’un corps rigide dans un écoulement bidimensionel d’un fluide visqueux incompressible avec conditions au bord de Navier et énergie infinie]
Marco Bravin1
1 Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence Cedex, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 303-319.

In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body’s boundary. The whole “viscous incompressible fluid + rigid body” system is assumed to occupy the full plane ℝ2. We prove the existence of global-in-time weak solutions with constant non-zero circulation at infinity.

Dans cet article, nous considérons le mouvement d’un corps rigide dans un fluide visqueux incompressible avec des conditions de glissement avec friction de Navier à l’interface. Le système “fluide+corps rigide” est supposé occuper le plan tout entier. Nous prouvons l’existence de solutions globales en temps avec une circulation constante non nulle à l’infini.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.36
Classification : 35Q30, 70E15, 76D05, 76D03

Marco Bravin 1

1 Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence Cedex, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Marco Bravin},
     title = {On the {2D} {\textquotedblleft}viscous incompressible fluid + rigid body{\textquotedblright} system with {Navier} conditions and unbounded energy},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {303--319},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     year = {2020},
     doi = {10.5802/crmath.36},
     language = {en},
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Marco Bravin. On the 2D “viscous incompressible fluid + rigid body” system with Navier conditions and unbounded energy. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 303-319. doi : 10.5802/crmath.36. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.36/

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