arXiv:1904.04795math.AP
Finite-Time Singularity Formation for $C^{1,α}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$
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Abstract
It has been known since work of Lichtenstein [42] and Gunther [29] in the 1920's that the $3D$ incompressible Euler equation is locally well-posed in the class of velocity fields with Hölder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.
> They should be able to describe the motion of any fluid under any circumstances — and for more than two centuries, they have. The Euler equations neglect viscosity. > They also assume that fluids are “incompressible,” meaning that under the rules of the Euler equations, you…
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