Concentration of mass in the pressureless limit of Euler equations for power law. (June 2019)

• Record Type: Journal Article
• Authors: Ibrahim, Muhammad; Liu, Fujun; Liu, Song
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 224
• Page End: 235
• Publication Date: 2019-06
• Subjects: Riemann solutions -- Delta wave -- Power law -- Zero pressure gas dynamics -- Weighted Dirac-measure -- Numerical simulations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.10.015
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, the limiting behavior of Riemann solutions to the Euler equations for compressible fluids in power law is studied as the adiabatic exponent goes to zero. We show that the limit solution forms the delta wave of the zero pressure gas dynamics in the distribution sense. At the end of the paper, we also give some numerical results to present the phenomena of concentration. Highlights: Delta wave, Riemann solutions. Formation of delta wave. Pressureless Limit of Euler equations. Zero pressure gas dynamics. Numerical simulations.