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math.AP2024
Self-similar instability and forced nonuniqueness: an application to the 2D Euler equations
Michele Dolce, Giulia Mescolini
Building on an approach introduced by Golovkin in the '60s, we show that nonuniqueness in some forced PDEs is a direct consequence of the existence of a self-similar linearly unsta…
math.AP2024
Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines
Michele Dolce, Carl Johan Peter Johansson, Massimo Sorella
We study the evolution of a passive scalar subject to molecular diffusion and advected by an incompressible velocity field on a 2D bounded domain. The velocity field is $u = \nabla…