3 problems

Taylor expansion conjecture. We conjecture that, as $r\to 0$,

Let $u_\varepsilon$ be a solution of the Ginzburg–Landau system in a smooth domain, and let $N_\varepsilon$ denote the boundary-energy quantity appearing in the regime of Theorem 1…

Let $psi(t,r,theta)=A(t,r)e^{imtheta}$ be a singular standing-vortex solution of the two-dimensional NLS with $sigma>2$, and let $psi_F$ denote the radial self-similar profile. Sup…