Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains. (English) Zbl 1430.35200
Summary: This paper is devoted to the study of the initial-boundary value problem for a multi-dimensional compressible Navier-Stokes-Poisson coupled system that describes the motion of a viscous gas with radiation, in the domain exterior to a ball of \(\mathbb{R}^d\). By means of nonlinear energy method, we show the global-in-time existence and asymptotic stability of the spherically and cylindrically symmetric solutions for large initial data, provided that the adiabatic exponent \(\gamma\) is sufficiently close to 1.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
35B40 | Asymptotic behavior of solutions to PDEs |
76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
80A21 | Radiative heat transfer |
Keywords:
viscous gas with radiation; spherical and cylindrical symmetry; asymptotic stability; large initial data; unbounded domainsReferences:
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