On the motion of a body with a cavity filled with compressible fluid

0503655 - MÚ 2020 RIV DE eng J - Journal Article
Galdi, G. P. - Mácha, Václav - Nečasová, Šárka
On the motion of a body with a cavity filled with compressible fluid.
Archive for Rational Mechanics and Analysis. Roč. 232, č. 3 (2019), s. 1649-1683. ISSN 0003-9527. E-ISSN 1432-0673
R&D Projects: GA ČR GA16-03230S
Institutional support: RVO:67985840
Keywords : compressible fluid * Navier-Stokes equations
OECD category: Pure mathematics
Impact factor: 2.420, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00205-018-01351-8

We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the coupled system body-fluid. Under suitable assumptions on the “mass distribution” of S, and for a sufficiently “small” Mach number and initial data, we show that every corresponding motion (in a suitable regularity class) must tend to a steady state where the fluid is at rest with respect to B. Moreover, S, as a whole, performs a uniform rotation around an axis parallel to the (constant) angular momentum of S, and passing through its center of mass.
Permanent Link: http://hdl.handle.net/11104/0295466