## On the evolution of compactly supported planar vorticity.(English)Zbl 0937.35137

The paper deals with the evolution of an ideal incompressible fluid vorticity with compact support. For planar fluids one demonstrates (taking into account not only the conservation of the moment of inertia but also the conservation of the center of mass), that the diameter of the support of nonnegative initial vorticity does not grow faster then $$O[ ( t\log t) ^{1/4}]$$ thus improving a previously known bound of order $$O( t^{1/3})$$. In the final section, an example is presented for which the support of the vorticity grows at a rate of $$O( t)$$.

### MSC:

 35Q35 PDEs in connection with fluid mechanics 76B47 Vortex flows for incompressible inviscid fluids 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids

### Keywords:

Euler equations; positive vorticity; Biot-Savart law