A Hamiltonian description of finite-time singularity in Euler's fluid equations (Q6095178)

In this work, the authors investigate a reduced model of Moffatt and Kimura (MK) which describes the interaction of two circular vortex rings. To extent that model representing Euler's ideal fluid equations of motion, firstly they discover two constants of motion for the MK model. One invariant serves as the Hamiltonian for its noncanonical Hamiltonian formulation, while the other turns out to be a Casimir invariant. Then they showed the existence of finite-time singularity. Explicitly, it is shown that within the proposed limits of applicability of the considered model, there exist solutions that blow up in finite time.