Global well posedness for the ghost effect system
type: Item
instance of: scholarly article
title: Global well posedness for the ghost effect system
zbMATH Open document ID: 1374.35277
author: Bilal Al Taki
published in: Communications on Pure and Applied Analysis
publication date: 2016-12-20T00:00:00Z
review text: 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.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 82D05
zbMATH DE Number: 6666337
zbMATH Keywords: ghost effect system
zbMATH Keywords: global existence
zbMATH Keywords: Navier-Stokes system
zbMATH Keywords: Euler equations
zbMATH Keywords: low Mach number
MaRDI profile type: Publication
full work available at URL: cpaa.2017017
OpenAlex ID: W2555170202
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DOI: 10.3934/CPAA.2017017
description: scientific article; zbMATH DE number 6666337