an:00841784
Zbl 0845.76017
Yang, Jianfu
Global vortex rings and asymptotic behaviour
EN
Nonlinear Anal., Theory Methods Appl. 25, No. 5, 531-546 (1995).
00027813
1995
j
76B47 35Q35
precompact minimizing sequences; existence theorem; steady axisymmetric vortex rings; vortex-strength parameter; direct variational method; constrained variational problem
The existence of solution is investigated in the case of steady axisymmetric vortex rings in an ideal fluid. The dependence between stream-function and vorticity is supposed to be known. The vortex-strength parameter and the propagation velocity of the vortex ring are prescribed as well. A direct variational method is used; it is proved that the corresponding functional is differentiable, and the minimizing sequences of a constrained variational problem are precompact. The main result on the asymptotic behaviour is that the cross-section of a steady vortex ring shrinks to a point, and the vortex ring degenerates into a singular circle as the vortex-strength parameter tends to infinity.
A.Berezovski (Tallinn)