中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人： Shao Feng(Peking University)

题  目：Self-similar algebraic spiral solutions for 2D Euler equations

时  间：2024.04.08（星期一）9:00-10:00

地  点：S813

摘 要：In this talk, we construct a large class of non-trivial self-similar solutions of the 2D incompressible Euler equations with self-similar initial vorticity data in the form of $|y|^{-\frac1\mu}\mathring{\omega}(\theta)$, where $\mathring{\omega}\in L^1(\TT)$. As a corollary, we prove the same result in the case where $\mathring{\omega}$ is a signed Radon measure on $\TT$. The solutions have vorticity forming algebraic spirals.