3 problems

Let $M\subset \mathbb{R}^3$ be a domain with the standard Euclidean metric, and let $u:M\to\mathbb{R}^3$ be a steady-state velocity field satisfying the stationary Euler equations.…

Consider the large-amplitude solution shown in panel (B), for which the stagnation point in the upper layer above the crest is very close to the interface. Corner formation conject…

Let $\theta=0$ in the infinite-wavelength case, and consider perturbative solutions of the steady Euler equations with piecewise constant vorticity. Bore conjecture. Perturbative s…