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 , with and for any , which can be embedded into the class of globally Lipschitz functions.
We prove a local in time well-posedness result in these classes and we are also 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.
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