UBC DG MP PDE Seminar: Evan Miller

In this talk, I will introduce the restricted Euler and hypodissipative Navier-Stokes equations. These equations are analogous to the Euler and hypodissipative Navier-Stokes equations, 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 for solutions that are odd, permutation symmetric, and mirror symmetric about the plane x1+x2+x3=0. The restricted Euler and hypodissipative Navier-Stokes equations respect both the energy equality and the identity for enstrophy growth for the full Euler and hypodissipative Navier–Stokes equations.