Extension of the Hoff solutions framework to cover compressible Navier-Stokes equations with possible anisotropic viscous tensor - ANR - Agence nationale de la recherche Accéder directement au contenu
Article Dans Une Revue Indiana University Mathematics Journal Année : 2023

Extension of the Hoff solutions framework to cover compressible Navier-Stokes equations with possible anisotropic viscous tensor

Résumé

In this paper, we construct global weak solutionsà la Hoff (i.e. intermediate regularity) for the compressible Navier-Stokes system governing a barotropic fluid with a pressure law p(ρ) = aρ γ where a > 0 and γ ≥ d/(4 − d)) and with an anisotropic fourth order symmetric viscous tensor with smooth coefficients under the assumption that the norms of the initial data (ρ0 − M, u0) ∈ L 2γ T d × (H 1 (T d)) d are sufficiently small, where M denotes the total mass of the fluid. We consider periodic boundary conditions for simplicity i.e. a periodic box Ω = T d with d = 2, 3 with |Ω| = 1. The main technical contribution of our paper is the extension of the Hoff solutions framework by relaxing the integrability needed for the initial density which is usually assumed to be L ∞ (T d). In this way, we are able to cover the case of viscous tensors that depend on the time and space variables. Moreover, when comparing to the results known for the global weak solutionsà la Leray (i.e. obtained assuming only the basic energy bounds), we obtain a relaxed condition on the range of admissible adiabatic coefficients γ.
Fichier principal
Vignette du fichier
BrBu_version17.pdf (305.74 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03342304 , version 1 (13-09-2021)

Identifiants

Citer

Didier Bresch, Cosmin Burtea. Extension of the Hoff solutions framework to cover compressible Navier-Stokes equations with possible anisotropic viscous tensor. Indiana University Mathematics Journal, 2023, 72 (5), pp.2145-2189. ⟨10.1512/iumj.2023.72.9559⟩. ⟨hal-03342304⟩
54 Consultations
64 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More