Conic Lagrangian Varieties and Localized Asymptotic Solutions of Linearized Equations of Relativistic Gas Dynamics

We study asymptotic solution of the Cauchy problem for the linearized system of relativistic gas dynamics. We assume that initial condiditiopns are strongly localized near a space-like surface in the Minkowsky space. We prove that the solution can be decomposed into three modes, corresponding to different routsb of the equations of characteristics. One of these roots is twice degenerate and the there are no focal points in the corresponding miode. The other two roots are simple; in order to describe the corresponding modes, we use the modificication of the Maslov’s canonical operator which was obtained recently.