3 problems

Marginal stability conjecture. Solutions of the Ginzburg–Landau equation with compactly supported initial data spread with asymptotic speed $2$.

For a forceless symmetric vortex configuration with correlation coefficient … where the central degree is $n_0=-\frac{N-1}{2}m$ and the other $N$ vortices have equal degree $m$, th…

Let $A$ be the annular domain, let $\mathcal{J}_{11}$ denote the admissible class of maps with prescribed degrees $(1,1)$, and let $u$ be the weak $H^1$ limit of a minimizing seque…