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

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 Hkk⩾3 solution only under...

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Autores principales:	Rong Shen, Yong Wang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/d2ccc0ddfd754099824804ef455e0bfb
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spelling	oai:doaj.org-article:d2ccc0ddfd754099824804ef455e0bfb2021-11-22T01:10:15ZOptimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation1687-913910.1155/2021/8636092https://doaj.org/article/d2ccc0ddfd754099824804ef455e0bfb2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8636092https://doaj.org/toc/1687-9139In 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 Hkk⩾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–Lq1⩽p⩽2,2⩽q⩽∞-type decay rates of the solution and its higher-order derivatives.Rong ShenYong WangHindawi LimitedarticlePhysicsQC1-999ENAdvances in Mathematical Physics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Rong Shen Yong Wang Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
description	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 Hkk⩾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–Lq1⩽p⩽2,2⩽q⩽∞-type decay rates of the solution and its higher-order derivatives.
format	article
author	Rong Shen Yong Wang
author_facet	Rong Shen Yong Wang
author_sort	Rong Shen
title	Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
title_short	Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
title_full	Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
title_fullStr	Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
title_full_unstemmed	Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation
title_sort	optimal lp–lq-type decay rates of solutions to the three-dimensional nonisentropic compressible euler equations with relaxation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/d2ccc0ddfd754099824804ef455e0bfb
work_keys_str_mv	AT rongshen optimallplqtypedecayratesofsolutionstothethreedimensionalnonisentropiccompressibleeulerequationswithrelaxation AT yongwang optimallplqtypedecayratesofsolutionstothethreedimensionalnonisentropiccompressibleeulerequationswithrelaxation
_version_	1718418370287632384

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

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