Investigation of finite-time singularity models of the Navier-Stokes equations*

Recently proposed low degree-of-freedom models [1] for describing the approach to finite-time singularity of the incompressible Navier-Stokes equations are investigated. These models assume an initial finite-energy configuration of two vortex rings placed symmetrically on two tilted planes. The noncanonical Hamiltonian structure [2] of the inviscid limit of the models will be presented and shown to elucidate the nature of the possible finite-time singularities in the model. \\ {\ } \\ \ [1] H. K.\ Moffatt and Y.\ Kimura, J.\ Fluid Mech.\ {\bf 861}, 930 (2019); {\bf 870\, R1}, (2019). \\ \ [2] P.\ J.\ Morrison, Rev.\ Mod.\ Phys.\ {\bf70}, 467 (1998).