The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces

The present paper is devoted to the study of a zero-Mach number system with heat conduction but no viscosity. We work in the framework of general non-homogeneous Besov spaces B p,r(R), with p ∈ [2, 4] and for any d ≥ 2, which can be embedded into the class of globally Lipschitz functions. We prove a local in time well-posedness result in these classes for general initial densities and velocity fields. Moreover, we are able to show a continuation criterion and a lower bound for the lifespan of the solutions. The proof of the results relies on Littlewood-Paley decomposition and paradifferential calculus, and on refined commutator estimates in Chemin-Lerner spaces.