# On the weak uniqueness of viscous incompressible fluid + rigid body'' system with Navier slip-with-friction conditions in a 2D bounded domain

Abstract : The existence of weak solutions to the viscous incompressible fluid + rigid body'' system with Navier slip-with-friction conditions in a 3D bounded domain has been recently proved by G\'{e}rard-Varet and Hillairet in \cite{exi:GeH}. In 2D for a fluid alone (without any rigid body) it is well-known since Leray that weak solutions are unique, continuous in time with $L^{2}$ regularity in space and satisfy the energy equality. In this paper we prove that these properties also hold for the 2D viscous incompressible fluid + rigid body'' system.
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https://hal.archives-ouvertes.fr/hal-01740859
Contributor : Marco Bravin Connect in order to contact the contributor
Submitted on : Thursday, March 22, 2018 - 2:35:27 PM
Last modification on : Saturday, March 24, 2018 - 1:05:25 AM
Long-term archiving on: : Thursday, September 13, 2018 - 8:23:06 AM

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UNINAVIERUPTOCOLLISION.pdf
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### Identifiers

• HAL Id : hal-01740859, version 1
• ARXIV : 1803.08765

### Citation

Marco Bravin. On the weak uniqueness of viscous incompressible fluid + rigid body'' system with Navier slip-with-friction conditions in a 2D bounded domain. 2018. ⟨hal-01740859⟩

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