Finite-time blow-up of a classical solution to the two-fluid model with density-dependent viscosity

This paper concerns the initial-boundary value problem for a compressible two-fluid model with density-dependent viscosities (possibly degenerating in vacuum), subject to Dirichlet boundary conditions. We prove that the two-fluid system with non-monotone pressure will blow up in finite time under the assumption that the initial densities include an isolated mass group.