Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-00794055
Contributor : Francesco Fanelli <>
Submitted on : Monday, February 25, 2013 - 12:01:14 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM
Long-term archiving on: : Sunday, April 2, 2017 - 4:47:13 AM

File

F-L_inviscid-mach.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00794055, version 1

Citation

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

Share

Metrics

Record views

172

Files downloads

98