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# 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: http://dx.doi.org/10.4310/CMS.2016.v14.n7.a11

#### Authors

#### 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