Local Existence And Formation Of Singularities For Regular Solutions To The Cauchy Problem Of One-dimensional Euler-Boltzmann Equations

This paper is focused on the study of the local existence and uniqueness of regularsolutions to the Cauchy problem for the one-dimensional Euler-Boltzmann equationsin radiation hydrodynamics, and the formation of singularities under the condition thatthe initial data contain local vacuum state. First we use induced processes and localthermodynamics equilibrium to transform Euler-Boltzmann equations into a simplerform. Then we transform this simple form into a symmetric hyperbolic system. Onthis basis, we obtain the existence of local classical solutions by using an iterationbased on the linearised problem and the Banach contraction mapping principle. Fromthis, we give the existence and uniqueness of regular solutions to the original problem.Finally, we prove that regular solutions will blow up in finite time if the initial datacontain local vacuum state.