Vortices, maximum growth and the problem of finite-time singularity formation

In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the question about the finite-time singularity formation in the 3D Navier–Stokes system and aims at a systematic identification of the most singular flow behaviors. We extend the results reported in Ayala and Protas …