Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions

Abstract

In this paper, we prove that the one-dimensional model of reactive micropolar real gas flow and thermal explosion has a solution locally in time. We first define the notion of a generalized solution for the governing initial-boundary value problem. We prove the claim of local existence by deriving a sequence of approximate problems obtained by Faedo-Galerkin projections. A priori estimates allow us to choose small enough time interval of existence, and show that the sequence of approximations is bounded in certain functional spaces, and therefore has a convergent subsequence. In the end, we show that it is precisely this limit that is the solution to the observed problem.