Communications in Mathematical Sciences

Volume 14 (2016)

Number 7

Non-relativistic and low mach number limits of two $P1$ approximation model arising in radiation hydrodynamics

Pages: 2023 – 2036

DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n7.a11

Authors

Jishan Fan (Department of Applied Mathematics, Nanjing Forestry University, Nanjing, China)

Fucai Li (Department of Mathematics, Nanjing University, Nanjing, China)

Gen Nakamura (Department of Mathematics, Hokkaido University, Sapporo, Japan)

Abstract

In this paper we study the non-relativistic and low Mach number limits of two $P1$ approximation model arising in radiation hydrodynamics in $\mathbb{T}^3$, i.e. the barotropic model and the Navier–Stokes–Fourier model. For the barotropic model, we consider the case that the initial data is a small perturbation of stable equilbria while for the Navier–Stokes–Fourier model, we consider the case that the initial data is large. For both models, we prove the convergence to the solution of the incompressible Navier–Stokes equations with/without stationary transport equations.

Keywords

radiation hydrodynamics, low Mach number limit, non-relativistic limit

2010 Mathematics Subject Classification

35B25, 35Q30, 35Q70

Published 14 September 2016