6 problems

Let $boldsymbol{u}^ u,boldsymbol{ abla}boldsymbol{\times}boldsymbol{u}^ u=boldsymbol{ abla}timesboldsymbol{u}^ u$ be a sequence of 2D Navier–Stokes solutions satisfying the paper's…

Let $u$ be an inviscid incompressible flow on $\mathbb{R}^2$ with scalar vorticity $\omega=\partial_1u^2-\partial_2u^1$, recovered from $\omega$ by the Biot–Savart law…

Let $W$ be a noise satisfying Assumption … {rm d} omega + operatorname{curl}^{-1} omegacdot nabla omega, {rm d} t + circ {rm d} Wcdot nabla omega = 0 … such that these stochastic 2…

Let $2<p<\infty$. Consider the two-dimensional Euler equation with initial velocity $v^\circ\in L^2$ and initial vorticity $\omega^\circ\in L^1\cap L^p$. A weak solution has veloci…

Let $M\subset\mathbb{R}^2$ be a bounded planar domain, let $\omega_0\in L^{\infty}(M)$ be initial vorticity, and let $\{\omega(t)\}_{t\in\mathbb{R}}$ be its inviscid incompressible…

Continuity conjecture. Kuksin measures are in fact supported on continuous vorticities.