Some spectral properties of the dynamical system managing the motion of rotating fluid
by
Saule D. Troitskaya
Moscow Institute of Steel and Alloys

We study the spectrum of the generator B of the group of motions of an ideal incompressible fluid in a rotating container G. It is well known that if G is a sphere or a cylinder then B has a complete system of eigenfunctions therefore all oscillations of the fluid are almost periodic functions of the time. We prove that for some class of axisymmetric domains G with edges the purely continuous spectrum of the operator B is not empty, so there exist non almost periodic motions of the rotating fluid.

This work was partially supported by the RFBR (Grant No 98-01-01000) and by the Programm of support of the leading scientific schools (Grant No 96-15-96091).

Date received: June 2, 1999