The well-posedness issue in endpoint spaces for an inviscid low-Mach number limit system - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

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

Résumé

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.
Fichier principal
Vignette du fichier
F-L_inviscid-mach.pdf (856.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00794055 , version 1 (25-02-2013)

Identifiants

  • HAL Id : hal-00794055 , version 1

Citer

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

Partager

Gmail Facebook X LinkedIn More