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arXiv · 1505.08137

Quasi-periodic non-stationary solutions of 3D Euler equations for incompressible flow

Sergey V. Ershkov
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Abstract

A novel derivation of non-stationary solutions of 3D Euler equations for incompressible inviscid flow is considered here. Such a solution is the product of 2 separated parts: - one consisting of the spatial component and the other being related to the time dependent part. Spatial part of a solution could be determined if we substitute such a solution to the equations of motion (equation of momentum) with the requirement of scale-similarity in regard to the proper component of spatial velocity. So, the time-dependent part of equations of momentum should depend on the time-parameter only. The main result, which should be outlined, is that the governing (time-dependent) ODE-system consist of 2 Riccati-type equations in regard to each other, which has no solution in general case. But we obtain conditions when each component of time-dependent part is proved to be determined by the proper elliptical integral in regard to the time-parameter t, which is a generalization of the class of inverse periodic functions.

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Sergey V. Ershkov. 2015-05-16. Quasi-periodic non-stationary solutions of 3D Euler equations for incompressible flow. https://doi.org/10.1016/j.jksus.2015.05.005

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