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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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/8636092 |
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| author | Rong Shen Yong Wang |
| author_facet | Rong Shen Yong Wang |
| author_sort | Rong Shen |
| collection | DOAJ |
| 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 |
| id | doaj-art-d2ccc0ddfd754099824804ef455e0bfb |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d2ccc0ddfd754099824804ef455e0bfb2025-02-03T06:46:18ZengWileyAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/8636092Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with RelaxationRong Shen0Yong Wang1South China Research Center for Applied Mathematics and Interdisciplinary StudiesSouth China Research Center for Applied Mathematics and Interdisciplinary StudiesIn 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.http://dx.doi.org/10.1155/2021/8636092 |
| spellingShingle | Rong Shen Yong Wang Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation Advances in Mathematical Physics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/8636092 |
| work_keys_str_mv | AT rongshen optimallplqtypedecayratesofsolutionstothethreedimensionalnonisentropiccompressibleeulerequationswithrelaxation AT yongwang optimallplqtypedecayratesofsolutionstothethreedimensionalnonisentropiccompressibleeulerequationswithrelaxation |