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Research

PDE Seminar

Small Scale Creation for 2D Water Waves

Speaker: Chenyun LUO（The Chinese University of Hong Kong）
Time: May 28, 2024, 17:00-18:00
Location: M616, College of Science Building

Abstract

We study the free boundary Euler equations modeling the motion of capillary water waves in 2D. We construct initial data with a flat initial interface and arbitrarily small velocity, such that the gradient of the vorticity grows at least double-exponentially for all times during the lifespan of the associated solution. This indicates that generic small rotational initial data will not lead to a small solution for all times, which is a sharp contrast to the irrotational water waves.