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Helical symmetry solutions for 3D incompressible Euler equations in an infinite cylinder

Daomin CAO (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Friday, August 18, 2023 - 3:00pm to 4:00pm
PDL C-38

In this talk the speaker will talk about some results on solutions for incompressible Euler equation. In particular those solutions whose vorticities are large and concentrated uniformly near a smooth curve \$ Γ(t) \$ embedded in entire \$R^3\$. This type of solutions, vortex filaments, are classical objects of fluid dynamics. Under suitable assumptions it is known to some extent that the curve evolves by its binormal flow. Two special kinds of binormal flows are traveling circle and rotating-translating helix. Solutions concentrating near a traveling circle is called vortex ring which have been studied extensively. In this talk, we will present existence of solutions near rotating-translating helix. The general case is called vortex filament conjecture which is still a well-known open problem. This talk is based on a joint paper with Wan Jie at Beijing University of Technology.

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