Steady vortex flows obtained from a constrained variational problem - B. Emamizadeh; M. H. Mehrabi (International Journal of Mathematics and Mathematical Sciences)
We prove the existence of steady two-dimensional ideal vortex flows occupying the first quadrant and containing a bounded vortex; this is done by solving a constrained variational problem. Kinetic energy is maximized subject to the vorticity, being a rearrangement of a prescribed function and subject to a linear constraint.