Vacuum states and global stability of rarefaction waves for compressible flow
The global stability of rarefaction waves for a broad class of entropy solutions containing vacuum (cavitation) states is proved for compressible Euler equations for one-dimensional both isentropic and non-isentropic fluids. In order to investigate the instability of solutions containing the vacuum states for compressible Navier-Stokes equations, the author presents some techniques to estimate the lower bound on the density for multidimensional viscous non-isentropic fluids with spherical symmetry between a solid core and a free boundary connected to a surrounding vacuum state. The analysis works for the solutions with arbitrary large oscillation.
scientific article; zbMATH DE number 1757305