On the motion of a rigid body in a two-dimensional irregular ideal flow

Olivier Glass (1) , Franck Sueur (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL - Laboratoire Jacques-Louis Lions

We consider the motion of a rigid body immersed in an ideal flow occupying the plane, with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time, in the spirit of the famous work by Yudovich for the fluid alone. We prove that if the body's boundary is Gevrey then the body's trajectory is Gevrey. This extends the previous work [Glass-Sueur-Takahashi 2010] to a case where the flow is irregular.

Mots clés: Ideal fluids; fluid-structure interaction

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Glass, Franck Sueur. On the motion of a rigid body in a two-dimensional irregular ideal flow. SIAM Journal on Mathematical Analysis, 2012, 44 (5), pp.3101-3126. ⟨10.1137/110839539⟩. ⟨hal-00605763v2⟩