Global Existence of Solutions to the Compressible Euler Equations with Time-dependent Damping and Logarithmic State Equation
Analysis of PDEs
2019-01-29 v2 Mathematical Physics
math.MP
Abstract
In mathematical physics, the pressure function is determined by the equation of state. There are two existing barotropic state equations: the state equation for polytropic gas with adiabatic index greater than or equal to 1 and the state equation for generalized Chaplygin gas in cosmology. In this paper, a logarithmic pressure is derived naturally with the coexistence of the two existing state equations through an equivalent symmetric hyperbolic transformation. On the study of the logarithmic pressure, global existence of solutions with small initial data to the one-dimensional compressible Euler equations with time-dependent damping is established.
Keywords
Cite
@article{arxiv.1807.00550,
title = {Global Existence of Solutions to the Compressible Euler Equations with Time-dependent Damping and Logarithmic State Equation},
author = {Ka Luen Cheung and Sen Wong},
journal= {arXiv preprint arXiv:1807.00550},
year = {2019}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:1204.4798 by other authors