On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2015

On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces

Résumé

We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in $\mathbb{R}^n.$ We focus on the so-called critical Besov regularity framework. In this setting, it is natural to consider initial densities $\rho_0,$ velocity fields $u_0$ and temperatures $\theta_0$ with $a_0:=\rho_0-1\in\dot B^{\frac np}_{p,1},$ $u_0\in\dot B^{\frac np-1}_{p,1}$ and $\theta_0\in\dot B^{\frac np-2}_{p,1}.$ After recasting the whole system in Lagrangian coordinates, and working with the \emph{total energy along the flow} rather than with the temperature, we discover that the system may be solved by means of Banach fixed point theorem in a critical functional framework whenever the space dimension is $n\geq2,$ and $1

Dates et versions

hal-01070461 , version 1 (01-10-2014)

Identifiants

Citer

Noboru Chikami, Raphaël Danchin. On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces. Journal of Differential Equations, 2015, 258, pp.3435-3467. ⟨10.1016/j.jde.2015.01.012⟩. ⟨hal-01070461⟩
56 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More