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The well-posedness issue in endpoint spaces for an inviscid low-Mach number limit system

Francesco Fanelli 1 Xian Liao 2, * 
* Corresponding author
2 Équations à dérivées partielles
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : The present paper is devoted to the well-posedness issue for a low-Mach number limit system with heat conduction but no viscosity. We will work in the framework of general Besov spaces B^s_{p,r}(R^d), d ≥ 2, which can be embedded into the class of Lipschitz functions. Firstly, we consider the case of p ∈ [2, 4], with no further restrictions on the initial data. Then we tackle the case of any p ∈ ]1, ∞], but requiring also a finite energy assumption. The extreme value p = ∞ can be treated due to a new a priori estimate for parabolic equations. At last we also briefly consider the case of any p ∈]1, ∞[ but with smallness condition on initial inhomogeneity. A continuation criterion and a lower bound for the lifespan of the solution are proved as well. In particular in dimension 2, the lower bound goes to infinity as the initial density tends to a constant.
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Preprints, Working Papers, ...
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Submitted on : Monday, February 25, 2013 - 12:01:14 AM
Last modification on : Saturday, January 15, 2022 - 4:13:42 AM
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  • HAL Id : hal-00794055, version 1


Francesco Fanelli, Xian Liao. The well-posedness issue in endpoint spaces for an inviscid low-Mach number limit system. 2013. ⟨hal-00794055⟩



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