3 problems

Let $M$ be the fluid domain, let $YU(M)$ denote the space of flows under consideration, and let $\mathscr{GM}$ be the set of generalized minimal flows: those $u\in YU(M)$ for which…

Consider the $\mu$-Hunter–Saxton equation on the circle, with initial momentum $\omega_0(x)$. $\mu$-Hunter–Saxton breakdown conjecture. Breakdown occurs if and only if the momentum…

Consider a one-dimensional Euler–Arnold equation on the circle, with Lagrangian flow $\eta(t,x)$, velocity $u(t,x)$, momentum operator $L$, and conserved momentum…