Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction

0542432 - MÚ 2022 RIV CH eng J - Journal Article
Caggio, M. - Kreml, Ondřej - Nečasová, Šárka - Roy, Arnab - Tang, T.
Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction.
Journal of Mathematical Fluid Mechanics. Roč. 23, č. 3 (2021), č. článku 50. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : Euler equations * fluid-rigid body interaction * measure-valued solutions * weak–strong uniqueness
OECD category: Pure mathematics
Impact factor: 1.907, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00021-021-00581-3

We consider a coupled system of partial and ordinary differential equations describing the interaction between an incompressible inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions which is generated by the vanishing viscosity limit of incompressible fluid–rigid body interaction system under some physically constitutive relations. Moreover, we show that the measure-valued solution coincides with strong solution on the interval of its existence. This relies on the weak-strong uniqueness analysis. This is the first result of an existence of measure-valued solution and weak-strong uniqueness in measure-valued sense in the case of inviscid fluid-structure interaction.
Permanent Link: http://hdl.handle.net/11104/0319841