Low Mach number limit for a compressible two-fluid model with algebraic closure and ill-prepared initial data in critical Besov spaces

In this paper, we study the low Mach number limit for a compressible two-fluid model with algebraic closure in the $d$-dimensional torus with $d \geq 2$. For large and ill-prepared initial data in critical Besov spaces, we prove that, provided that the Mach number is sufficiently small, the rescaled