تقرير
Explicit solutions to the 3D incompressible Euler equations in Lagrangian formulation
| العنوان: | Explicit solutions to the 3D incompressible Euler equations in Lagrangian formulation |
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| المؤلفون: | Saleva, Tomi, Tuomela, Jukka |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Physics (Other) |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Physics - Fluid Dynamics, 35A09, 35Q31, 76B99 |
| الوصف: | We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this study. We search for solutions where the time component and the spatial component are separated, applying the same ideas we used previously in the two dimensional case. We show a general method to derive separate constraint equations for the spatial component and the time component. Using this provides us with a plenty of solution sets exhibiting several different types of fluid behaviour, but since they are computationally heavy to analyze, we have to restrict deeper analysis to the most interesting cases only. It is also possible and perhaps even probable that there exist more solutions of the separation of variables type beyond what we have found. Comment: 22 pages, 0 figures, submitted to The Journal of Mathematical Fluid Mechanics |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00021-022-00731-1 |
| URL الوصول: | http://arxiv.org/abs/2202.00398 |
| رقم الأكسشن: | edsarx.2202.00398 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00021-022-00731-1 |
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