Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density
文献类型：期刊论文
| 作者 | Chen, Gui-Qiang G.1; Wang, Yong2
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| 刊名 | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
 |
| 出版日期 | 2022-03-01 |
| 卷号 | 243期号:3页码:1699-1771 |
| ISSN号 | 0003-9527 |
| DOI | 10.1007/s00205-021-01742-4 |
| 英文摘要 | We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density so that the total initial-energy is unbounded. The central feature of the solutions is the strengthening of waves as they move radially inward toward the origin. For the large initial data of positive far-field density, various examples have shown that the spherically symmetric solutions of the Euler equations blow up near the origin at a certain time. A fundamental unsolved problem is whether the density of the global solution would form concentration to become a measure near the origin for the case when the total initial-energy is unbounded and the wave propagation is not at finite speed starting initially. In this paper, we establish a global existence theory for spherically symmetric solutions of the compressible Euler equations with large initial data of positive far-field density and relative finite-energy. This is achieved by developing a new approach via adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the vanishing viscosity limit of global weak solutions of the Navier-Stokes equations with the density-dependent viscosity terms to the corresponding global solution of the Euler equations with large initial data of spherical symmetry and positive far-field density can be obtained. One of our main observations is that the adapted class of degenerate density-dependent viscosity terms not only includes the viscosity terms for the Navier-Stokes equations for shallow water (Saint Venant) flows but also, more importantly, is suitable to achieve the key objective of this paper. These results indicate that concentration is not formed in the vanishing viscosity limit for the Navier-Stokes approximations constructed in this paper even when the total initial-energy is unbounded, though the density may blow up near the origin at certain time and the wave propagation is not at finite speed. |
| 资助项目 | UK Engineering and Physical Sciences Research Council[EP/L015811/1] ; UK Engineering and Physical Sciences Research Council[EP/V008854/1] ; Royal Society-Wolfson Research Merit Award (UK) ; National Natural Sciences Foundation of China[12022114] ; National Natural Sciences Foundation of China[11771429] ; National Natural Sciences Foundation of China[11671237] ; National Natural Sciences Foundation of China[11688101] |
| WOS研究方向 | Mathematics ; Mechanics |
| 语种 | 英语 |
| WOS记录号 | WOS:000750982100001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59962]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Chen, Gui-Qiang G. |
| 作者单位 | 1.Univ Oxford, Math Inst, Oxford OX2 6GG, England 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chen, Gui-Qiang G.,Wang, Yong. Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2022,243(3):1699-1771. |
| APA | Chen, Gui-Qiang G.,&Wang, Yong.(2022).Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,243(3),1699-1771. |
| MLA | Chen, Gui-Qiang G.,et al."Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 243.3(2022):1699-1771. |
入库方式： OAI收割
来源：数学与系统科学研究院
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