4 problems

Consider fractional Brownian motions with Hurst parameter $H\in (1/2,1)$ as intermediate processes between smooth and Brownian-semimartingale vortex filaments, and assume that the…

Let $u$ be a smooth solution of the incompressible Euler equations in $4\mathbb{R}^3$ whose vorticity is initially concentrated near a smooth curve. Let the curve evolve according…

Spectrum-equality conjecture. Even though necessarily $\alpha_{x_0}(t)\neq\alpha_0(t)$, one has

Large-$D$ stability conjecture. In the limit $D\rightarrow\infty$, the only energetically stable equilibrium is the $q=1$ ring.