| Abstract: |
| In this talk I will focus on two results justifying the low Mach Number limit for the compressible two-fluid system in the regime of strong and weak solutions. In the framework of local-in-time strong solutions, we prove that, for well-prepared initial data, solutions to the rescaled compressible two-fluid system exist on a time interval independent of the Mach number and converge to the solution of the incompressible Navier--Stokes equations as the Mach number tends to zero.
In the framework of weak solutions, our recently developed method of relative entropies, can be applied to identify the inhomogeneous incompressible Navier--Stokes equations as the limiting system when the Mach number goes to zero, even in the ill-prepared data case. The proof is based on the relative entropy method and the dispersive estimates of the acoustic waves. |
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