Optimal Lp–Lq‐Type Decay Rates of Solutions to the Three‐Dimensional Nonisentropic Compressible Euler Equations with Relaxation

Rong Shen and Yong Wang

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

Abstract: In this paper, we consider the three‐dimensional Cauchy problem of the nonisentropic compressible Euler equations with relaxation. Following the method of Wu et al. (2021, Adv. Math. Phys. Art. ID 5512285, pp. 1–13), we show the existence and uniqueness of the global small Hk(k⩾3) solution only under the condition of smallness of the H3 norm of the initial data. Moreover, we use a pure energy method with a time‐weighted argument to prove the optimal Lp–Lq(1 ⩽ p ⩽ 2, 2 ⩽ q⩽∞)‐type decay rates of the solution and its higher‐order derivatives.

Date: 2021
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https://doi.org/10.1155/2021/8636092

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:8636092

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