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タイトル: | Characterization of Three-Dimensional Euler Flows Supported on Finitely Many Fourier Modes |
著者: | Kishimoto, Nobu ![]() ![]() ![]() Yoneda, Tsuyoshi |
著者名の別形: | 岸本, 展 米田, 剛 |
キーワード: | Three-dimensional incompressible Euler flow Finitely many Fourier modes Characterization Beltrami flow 35Q31 76B03 |
発行日: | Aug-2022 |
出版者: | Springer Nature |
誌名: | Journal of Mathematical Fluid Mechanics |
巻: | 24 |
号: | 3 |
論文番号: | 74 |
抄録: | Recently, the Nash-style convex integration has been becoming the main scheme for the mathematical study of turbulence, and the main building block of it has been either Beltrami flow (finite mode) or Mikado flow (compactly supported in the physical side). On the other hand, in physics, it is observed that turbulence is composed of a hierarchy of scale-by-scale vortex stretching. Thus our mathematical motivation in this study is to find another type of building blocks accompanied by vortex stretching and scale locality (possibly finitely many Fourier modes). In this paper, we give a complete list of solutions to the 3D Euler equations with finitely many Fourier modes, which is an extension of the corresponding 2D result by Elgindi et al. (Comm Math Phys 355(1): 145–159, 2017). In particular, we show that there are no 3D Euler flows with finitely many Fourier modes, except for stationary 2D-like flows and Beltrami flows. We also discuss the case when viscosity and Coriolis effect are present. |
著作権等: | This is a post-peer-review, pre-copyedit version of an article published in 'Journal of Mathematical Fluid Mechanics'. The final authenticated version is available online at: https://doi.org/10.1007/s00021-022-00703-5. The full-text file will be made open to the public on 15 June 2023 in accordance with publisher's 'Terms and Conditions for Self-Archiving'. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/276192 |
DOI(出版社版): | 10.1007/s00021-022-00703-5 |
関連リンク: | https://arxiv.org/abs/2110.08039 |
出現コレクション: | 学術雑誌掲載論文等 |
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