Low-Mach-number limit of a compressible two-phase flow system with algebraic closure
We analyse a bi-fluid isentropic compressible Navier-Stokes system with barotropic pressure laws in a two-phase framework with equal pressure and single velocity. We focus on the rigorous analysis of the low Mach number limit under well-prepared initial data. Our main result shows that, as the Mach number tends to zero, the partial densities converge to constant states while the velocity field converges to a divergence-free vector field, and we recover the incompressible non-homogenous fluid system. The volume fractions remain nontrivial and are transported by the limit flow. Our method relies on the introduction of suitable modulated quantities and on two relative entropy functionals adapted to the two-phase structure: a standard entropy commonly used in the literature, and a logarithmic entropy, which is essential here as the former is not sufficient due to the structure of the underlying two-phase system.