3 problems

Let $\omega$ and $u$ solve the De Gregorio model … where $H$ is the Hilbert transform and $\Lambda^{-1}$ is defined by the displayed relation. De Gregorio's global regularity conje…

Consider the nonlocal transport equation … allows for non-uniqueness. The paper leaves the question for future investigation; multiple weak solutions are known when the support of…

The model concerns initial data with components $b_j^0$ satisfying the adjacent-scale condition $b_j^0\leq\sqrt{2}b_{j+1}^0$ for sufficiently large indices. Eventual adjacent-scale…