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

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 HNN≥3 solution; in particular, we only require that the H4 norms of the initial data be small when N≥5. Moreover, we use...

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Main Authors: Yunshun Wu, Yong Wang, Rong Shen
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/5512285
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author Yunshun Wu
Yong Wang
Rong Shen
author_facet Yunshun Wu
Yong Wang
Rong Shen
author_sort Yunshun Wu
collection DOAJ
description 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 HNN≥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.
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spelling doaj-art-ee27e0776ea74fd2b640f0aefccd4d982025-08-20T03:20:44ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/55122855512285Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3Yunshun Wu0Yong Wang1Rong Shen2School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaSouth China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaSouth China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaWe 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 HNN≥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.http://dx.doi.org/10.1155/2021/5512285
spellingShingle Yunshun Wu
Yong Wang
Rong Shen
Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
Advances in Mathematical Physics
title Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
title_full Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
title_fullStr Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
title_full_unstemmed Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
title_short Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ3
title_sort global existence and long time behavior of solutions to the full compressible euler equations with damping and heat conduction in r3
url http://dx.doi.org/10.1155/2021/5512285
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AT yongwang globalexistenceandlongtimebehaviorofsolutionstothefullcompressibleeulerequationswithdampingandheatconductioninr3
AT rongshen globalexistenceandlongtimebehaviorofsolutionstothefullcompressibleeulerequationswithdampingandheatconductioninr3