A note on the well-posedness of the compressible viscous fluid in the critical Besov space (Regularity and Singularity for Partial Differential Equations with Conservation Laws)

"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 2015. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We prove well-posedness of the compressible Navier-Stokes system in the Lagrangian formulation by the use of absolute temperature. The purpose of this article is to illustrate the difference between the use of the total energy along the flow in Chikami-Danchin [3] (J. Difff. Eq, 258 (2015), 3435-3467) and the absolute temperature