no code implementations • 18 Jan 2022 • Yongji Wang, Ching-Yao Lai, Javier Gómez-Serrano, Tristan Buckmaster
Whether there exist finite time blow-up solutions for the 2-D Boussinesq and the 3-D Euler equations are of fundamental importance to the field of fluid mechanics.
no code implementations • 8 Dec 2020 • Javier Gómez-Serrano, Jaemin Park, Jia Shi, Yao Yao
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $\Omega$, such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles.
Analysis of PDEs
