Global Existence and Long‐Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3

Yunshun Wu, Yong Wang and Rong Shen

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: We study the Cauchy problem of the three‐dimensional full compressible Euler equations with damping and heat conduction. We prove the existence and uniqueness of the global small HN(N ≥ 3) solution; in particular, we only require that the H4 norms of the initial data be small when N ≥ 5. Moreover, we use a pure energy method to show that the global solution converges to the constant equilibrium state with an optimal algebraic decay rate as time goes to infinity.

Date: 2021
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https://doi.org/10.1155/2021/5512285

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:5512285

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