Abstract
AbstractWe 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.
Funder
Suomen Kulttuurirahasto
University of Eastern Finland (UEF) including Kuopio University Hospital
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Cited by
1 articles.
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