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In this paper we prove global in time existence of weak solutions to zeroMach number systems arising in fluid mechanics. Relaxing a certain algebraicconstraint between the viscosity and the conductivity introduced in [D. Bresch,E.H. Essoufi, and M. Sy, J. Math. Fluid Mech. 2007] gives a more completeanswer to an open question formulated in [P.-L. Lions, Oxford 1998]. A newmathematical entropy shows clearly the existence of two-velocity hydrodynamicswith a fixed mixture ratio. As an application of our result we first discuss amodel of gaseous mixture extending the results of [P. Embid, Comm. PartialDiff. Eqs. 1987] to the global weak solutions framework. Second, we present theghost effect system studied by [C.D. Levermore, W. Sun, K. Trivisa, SIAM J.Math. Anal. 2012] and discuss a contribution of the density-dependentheat-conductivity coefficient to the issue of existence of weak solutions.

Two-velocity hydrodynamics in fluid mechanics: Part I Well posedness for zero Mach number systems