| 概要 | Knotted and linked geometric structures have long played a
relevant role in fluid mechanics. In this talk we will review
some results in this direction, focusing on the recent work of
the speaker and D. Peralta-Salas on the existence of knotted and
linked vortex lines and (thin) vortex tubes in steady solutions
to the Euler equation in R^3. In the first part of the talk we
will present the generalities of these results and discuss the
main principles that lie behind the demonstration. The second
part will focus of technical aspects of the proofs, where we
will discuss the interplay between ideas of dynamical systems
and partial differential equations. |