On an initial boundary value problem for gas dynamics in thermal nonequilibrium

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For gas dynamics with several thermal nonequilibrium modes, the global existence of smooth solutions to an initial boundary value problem is established. The key difference compared with the initial value problem studied by Zeng [Arch. Ration. Mech. Anal. 150, 225–279 (1999); ibid. 196, 191–225 (2010)] is the boundary effects, e.g., boundary layers. Moreover, the exponential decay of solutions to an initial boundary value problem of the linearized system with a vibrational nonequilibrium mode is proved via the Fourier analysis, which illustrates a key distinction from that for the initial value problem without a boundary for which the decay is only algebraic.