We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-point argument. In the second case, we prove non-existence of such solutions using weighted energy estimates.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics