On the 2D “viscous incompressible fluid + rigid body” system with Navier conditions and unbounded energy

Bravin, Marco

Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 303-319.

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.

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 ${ℝ}^2$. We prove the existence of global-in-time weak solutions with constant non-zero circulation at infinity.

Classification : 35Q30, 70E15, 76D05, 76D03

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