BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Liouville Chain Solutions of the Euler Equation - Vikas Krishnamur
 thy (Indian Institute of Technology)
DTSTART:20230727T140000Z
DTEND:20230727T143000Z
UID:TALK202816@talks.cam.ac.uk
DESCRIPTION:We describe a large class of solutions of the two-dimensional 
 steady incompressible Euler equation in which point vortices are embedded 
 in a non-constant background vorticity field such that the whole arrangeme
 nt is stationary. This background vorticity is proportional to the exponen
 tial of the stream function and leads to a Liouville-type partial differen
 tial equation. We exploit the known solution structure of a class of solut
 ions of this Liouville-type equation to construct solutions\, which we cal
 l Liouville chains\, of the Euler equation mentioned above. Liouville chai
 ns can be constructed as iterated solutions starting from a simple purely 
 point vortex equilibrium (without a background field). Each iteration form
 s one link in the chain and can terminate after one step\, a finite number
  of steps\, or go on indefinitely. The solutions are given in terms of an 
 arbitrary positive real parameter\, and as this parameter goes to zero or 
 infinity\, we find that the background vorticity concentrates into point v
 ortices\, and in the limit the solutions go over into purely point vortex 
 equilibria. The solutions also contain arbitrary complex-valued parameters
  which arise as integration constants in the iteration. We describe severa
 l examples illustrating all these properties.\n(Joint work with Miles Whee
 ler\, Darren Crowdy\, and Adrian Constantin)
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR