The Euler Equations and Non-Local Conservative Riccati Equations
Peter Constantin
TL;DR
This paper discusses a family of exact solutions to the 3D Euler equations that exhibit finite-time blow-up and infinite kinetic energy, highlighting complex behaviors in fluid dynamics.
Contribution
It introduces an infinite-dimensional family of solutions to the Euler equations, expanding understanding of finite-time singularities in fluid flows.
Findings
Solutions blow up in finite time
Solutions have infinite kinetic energy
Provides insight into singularity formation in fluids
Abstract
We present an infinite dimensional family of of exact solutions of the incompressible three-dimensional Euler equations. These solutions, proposed by Gibbon and Ohkitani, have infinite kinetic energy and blow up in finite time.
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Taxonomy
TopicsNavier-Stokes equation solutions · Fluid Dynamics and Turbulent Flows · Computational Fluid Dynamics and Aerodynamics