3 problems

Let $m$ be the number of branches in an $m$-fold symmetric algebraic spiral vortex sheet solution of the two-dimensional incompressible Euler equations, with…

Almost-everywhere geometric-constraint conjecture. The geometric constraint $$ is satisfied for almost all values of $a>0$ and $\alpha\in (0,1/2a)\cup (1/2a,\infty)$, rather than o…

A vortex sheet is a solution of the two-dimensional incompressible Euler equation whose velocity field is discontinuous across an interface; here the initial interface data are ass…