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Vortex stretching in head-on collision of vortex rings

PDE and Applied Math Seminar

Speaker: In-Jee Jeong, Korea Institute for Advanced Study
Location: Zoom
Start time: Thu, Mar 31 2022, 4:10PM

We investigate the head-on collision scenario of antiparallel vortex rings using the axisymmetric Euler equations. Under no-swirl and sign assumptions on the initial vorticity, we obtain a universal lower bound on the vortex impulse growth for all times. Key ingredients are special monotonicity formulas and interpolation inequalities involving conserved and monotone quantities of the fluid. As a consequence, we obtain various infinite norm growth results for solutions to the Euler equations, including infinite vortex stretching in infinite time. (Joint work with Kyudong Choi, UNIST.)