Publikace na Matematicko-fyzikální fakulta |
2022
Abstrakt
We prove the existence of a weak solution to the compressible Navier-Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport equation.
We then prove that the "stiff pressure" limit gives rise to the two-phase compressible/incompressible system with congestion constraint describing the free interface. We prescribe the velocity at the boundary and the value of density at the inflow part of the boundary of a general bounded C-2 domain.
For the positive velocity flux, there are no restrictions on the size of the boundary conditions, while for the zero flux, a certain smallness is required for the last limit passage.