Global well posedness for the ghost effect system
This paper is devoted to the proof of the global in time existence of solutions to the, so called, ghost system effect (cf. [\textit{C. D. Levermore} et al., SIAM J. Math. Anal. 44, No. 3, 1760--1807 (2012; Zbl 1251.35046)]) when both the Euler equations and the Navier-Stokes equations fail to describe the behavior of a gas in the hydrodynamic limit of Boltzmann equation, and quantities of the order of the Knudsen number affect the behavior of the gas. The analysis involves a new functional inequality similar to that in a recent study of on compressible Navier-Stokes system with degenerate viscosities (inspired by [\textit{A. Jüngel} and \textit{D. Matthes}, SIAM J. Math. Anal. 39, No. 6, 1996--2015 (2008; Zbl 1160.35428)]), and a construction in [\textit{D. Bresch} et al., J. Math. Pures Appl. (9) 104, No. 4, 762--800 (2015; Zbl 1359.35126)] for low Mach number system.
scientific article; zbMATH DE number 6666337
scientific article