Seminar on partial differential equations

Body with a Cavity Filled with a Compressible Fluid

We  study  the  dynamics  of  a  system  composed  by a rigid body containing a visous compressible fluid. The  emphasis  is  laid  upon  the  analysis  of  the  long time behavior of the whole system.  We show that for small initial data the whole system tends to a permanent rotation similarly as in the incompressible case. On the other hand, we highlight some problems coming from compressibility which do not allow to prove the same for solutions emanating from arbitrary initial data.
The work was done in collaboration with G. P. Galdi and S. Necasova