Exact, infinite energy, blowup solutions of the threedimensional Euler equations
Abstract
For the class of cylindrically symmetric velocity fields U (r, z, t) = {u(r, t), v(r, t), zgamma(r, t)},
two infinite energy exact solutions of the threedimensional incompressible Euler equations are exhibited that blow up at every point in space in finite time. The first solution is embedded within the second as a special case and in both cases v = 0. Both solutions represent threedimensional vortices which take the form of hollow cylinders for which the vorticity vector is bold omega = (0, omega_{theta}, 0). An analysis on characteristics shows how more general solutions can be constructed and analysed.
 Publication:

Nonlinearity
 Pub Date:
 September 2003
 DOI:
 10.1088/09517715/16/5/315
 Bibcode:
 2003Nonli..16.1823G