Blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations

Abstract

In this paper, we study the blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations of radiation hydrodynamics. First, we improve the blowup result in [P. Jiang and Y. G. Wang, Initial-boundary value problems and formation of singularities for one-dimensional non-relativistic radiation hydrodynamic equations, J. Hyperbolic Differential Equations 9 (2012) 711–738] on the half line [Formula: see text] for large initial data by removing a restrict condition. Next, we obtain a new blowup result on the half line [Formula: see text] by introducing a new momentum weight. Finally, we present two non-global existence results for the smooth solutions to the one-dimensional Euler–Boltzmann equations with vacuum on the interval [Formula: see text] by introducing some new average quantities.