8 problems

Stability conjecture. A ring of $N$ low-pressure systems is Lyapunov stable for $N=3,4,5$. A ring of $N=3,4,5,6$ low-pressure systems together with a weak polar high-pressure syste…

Let $M$ be a smooth closed surface, and consider two point vortices on $M$ whose separation is infinitesimal and whose vorticities are equal in magnitude and opposite in sign. Kimu…

Consider $N$ vortex rings with radii of order $|\log\varepsilon|^\alpha$ as $\varepsilon\to0$, where $\alpha>2$, and let $z_i(t)$ denote the positions of the corresponding vortices…

Marchioro–Pulvirenti conjecture. The set of collapses ${\mathfrak C}$ has Lebesgue measure $0$.

A vortex patch is a vorticity distribution of the form $\omega(x,t)=\lambda I_{A_t}$, where $\lambda\in\mathbb R$ is the vorticity strength and $A_t\subset\mathbb R^2$ is the patch…

Point-vortex limit conjecture. A massive particle moves according to

For the point-vortex system under discussion, let $\sum_{i \neq j}\Gamma_i\Gamma_j=0$, the parameter value at which the stability behavior changes in the corresponding planar and s…

Let $N$ symplectic point vortices evolve on the phase space $(\mathbb R^{2m})^N$, where $m>1$, and interpret complete integrability in the Arnold–Liouville sense. Non-integrability…