Globally bounded trajectories for the barotropic Navier–Stokes system with general boundary conditions

Abstract

We consider the barotropic Navier–Stokes system describing the motion of a viscous compressible fluid interacting with the outer world through general in/out flux boundary conditions. We consider a hard-sphere type pressure EOS and show that all trajectories eventually enter a bounded absorbing set. In particular, the associated $\omega -$limit sets are compact and support a stationary statistical solution.

Keywords:

• Absorbing set
• compressible Navier–Stokes system
• energetically open system
• in/out flux boundary conditions

MSC:

• 35Q30
• 37L15
• 76N15

Additional information

Funding

The work of E.F. was partially supported by the Czech Sciences Foundation (GAČR), Grant Agreement 18-05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.