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arXiv · 2107.03118

On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity

Guocai Cai·Yanfang Peng·Yi Peng
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Abstract

We consider the one-dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the stress-free boundary condition, which reveals the motion of a viscous heat-conducting perfect polytropic gas with adiabatic ends putting into a vacuum. We prove that the solution of one dimensional compressible Navier-Stokes system with the stress-free boundary condition shares the same large-time behavior as the case of constant heat conductivity.

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Guocai Cai, Yanfang Peng, Yi Peng. 2021-07-07. On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity. https://doi.org/10.1016/j.jde.2022.01.051

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