On the steady states of 2D incompressible Euler Equations near the Bahouri-Chemin Patch
Yupei Huang
2023-08-03 15:00-16:00
MCM110
Speaker: Yupei Huang (Duke University)Time: 15:00-16:00 August 3, 2023 (Thursday)
Place: MCM110
Title: On the steady states of 2D incompressible Euler Equations near the Bahouri-Chemin Patch
Abstract: The Bahouri-Chemin patch is an important singular steady-state for 2D incompressible Euler equations in the flat torus. In this talk, we consider steady states near the Bahouri-Chemin patch. More precisely, we use two different ways to approximate the semi-linear elliptic equations describing the Bahouri-Chemin patch. In one way, we get smooth steady states close to the Bahouri-Chemin patch in the sense of the Holder norm of the velocity field. It,in particular, shows the importance of non-vanishing condition for vorticity on the boundary in the example of double expenential growth for gradient of vorticity. In the other way, we obtain singular steady states near the Bahouri-Chemin in the sense of the continuous norm of the velocity field. In those examples, an interesting feature is there are multiple paticle trajectories across the origin.This is joint work with Tarek Elgindi.
