Аннотация
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.
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