Online Talk 

Beltrami fields curl u=f u, div  u=0 appear as steady states of ideal incompressible flows or plasma equilibria. I will discuss existence and non-existence issues on them for non-constant factor f. In the first half of the talk, I will discuss existence of axisymmetric Beltrami fields forming vortex rings and their construction via a variational principle. In the second half, I will discuss a rigidity problem on symmetry of u for symmetric f.