Pointwise structure of a radiation hydrodynamic model in one‐dimension

In this paper, we study the nonlinear stability and the pointwise structure around a constant equilibrium for a radiation hydrodynamic model in 1‐dimension, in which the behavior of the fluid is described by a full Euler equation with certain radiation effect. It is well‐known that the classical solutions of the Euler equation in 1‐D may blow up in finite time for general initial data. The global existence of the solution in this paper means that the radiation effect stabilizes the system and prevents the formation of singularity when the initial data is small. To study the precise effect of the radiation in this model, we also treat the pointwise estimates of the solution for the original nonlinear problem by combining the Green's function for the linearized radiation hydrodynamic equations with the Duhamel's principle. The result in this paper shows that the pointwise structure of this model is similar to that of full Navier‐Stokes equations in 1‐D.