7 problems

Hydrodynamical Weinstein conjecture. Every smooth rotational Beltrami flow on a Riemannian three-manifold has a closed orbit.

Conjecture on rotational Beltrami fields on $T^3$. Every $C^\infty$ rotational Beltrami field on $T^3$ has a contractible closed flowline.

Beltrami fields are vector fields $u$ satisfying … where $\alpha$ is constant in the strong Beltrami case. Chaotic dynamics conjecture. Beltrami fields should exhibit chaotic dynam…

Let $X\in\mathscr B(\mathbb R^3)$ be a Beltrami field, and let a periodic saddle orbit of $X$ have a homoclinic tangency. A homoclinic tangency is non-degenerately unfolded in…

A Beltrami field is a vector field $u$ on $\mathbb{R}^3$ or the flat torus $\mathbb{T}^3$ satisfying … for some nonzero constant $\lambda$. An energy level is the restriction of a…

Beltrami-field proportionality conjecture. Nonconstant proportionality factors $f$ admitting a nonzero Beltrami field have the following properties:

A Beltrami field is a vector field $u$ on $\mathbb{R}^3$ satisfying … for some nonzero constant $\lambda$. A divergence-free vector field is a vector field with…