Georgia Institute of Technology College of Sciences

In this talk, I will introduce the Fourier-restricted Euler and hypodissipative Navier–Stokes equations. These equations are analogous to the Euler equation and hypodissipative Navier–Stokes equation, respectively, but with the Helmholtz projection replaced by a projection onto a more restrictive constraint space. The nonlinear term arising from the self-advection of velocity is otherwise unchanged. I will prove finite time-blowup when the dissipation is weak enough, by making use of a permutation symmetric Ansatz that allows for a dyadic energy cascade of the type found in the Friedlander-Katz-Pavlović dyadic Euler/Navier–Stokes model equation.