  In this paper we prove global in time existence of weak solutions to zero
Mach number systems arising in fluid mechanics. Relaxing a certain algebraic
constraint between the viscosity and the conductivity introduced in [D. Bresch,
E.H. Essoufi, and M. Sy, J. Math. Fluid Mech. 2007] gives a more complete
answer to an open question formulated in [P.-L. Lions, Oxford 1998]. A new
mathematical entropy shows clearly the existence of two-velocity hydrodynamics
with a fixed mixture ratio. As an application of our result we first discuss a
model of gaseous mixture extending the results of [P. Embid, Comm. Partial
Diff. Eqs. 1987] to the global weak solutions framework. Second, we present the
ghost effect system studied by [C.D. Levermore, W. Sun, K. Trivisa, SIAM J.
Math. Anal. 2012] and discuss a contribution of the density-dependent
heat-conductivity coefficient to the issue of existence of weak solutions.
