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arXiv · 1403.0960

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

Francesco Fanelli·Xian Liao
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Abstract

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 $B^s_{p,r}(\mathbb{R}^d)$, with $p\in[2,4]$ and for any $d\geq 2$, 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.

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Francesco Fanelli, Xian Liao. 2014-03-04. The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces. https://arxiv.org/abs/1403.0960

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