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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| 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. |
| format | Article |
| id | doaj-art-ee27e0776ea74fd2b640f0aefccd4d98 |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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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