Affiliations: [a] Institut de Mathématiques de Jussieu-Paris Rive Gauche – UMR 7586, Université Paris-Diderot, Paris, France. E-mail: francesco.fanelli@imj-prg.fr | [b] Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, China. E-mail: xian.liao@amss.ac.cn
Correspondence:
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Corresponding author: Xian Liao, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, 55 Zhongguancun East Road, 100190 Beijing, China. Tel.: +86 10 82541519; Fax: +86 10 82541591; E-mail: xian.liao@amss.ac.cn.
Note: [*] Present address: Centro di Ricerca Matematica “Ennio De Giorgi”, Scuola Normale Superiore, Collegio Puteano, Piazza dei Cavalieri, 3, 56126 Pisa, Italy.
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 Bp,rs(Rd), 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 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.
