On the Discretely Self-similar Solutions to the Euler Equations in R3

We remove (alpha, lambda)-discretely self-similar blow up for solutions to the Euler equations for alpha >= 3/2, for which we allow sublinear growth for the profile. More precisely, we show that there are only spatial constant (alpha, lambda)-discretely self-similar solutions v = c(t) having the sublinear growth at the infinity. For the proof, we establish a new a priori L-loc(2)(R-3) estimate for the 3D Euler equations.

Automated summary

This study focuses on the (alpha, lambda)-discretely self-similar blow up for solutions to the Euler equations for alpha >= 3/2, where sublinear growth is allowed for the profile. It is shown that there are only spatial constant (alpha, lambda)-discretely self-similar solutions with sublinear growth at infinity. A new a priori L-loc(2)(R-3) estimate for the 3D Euler equations is established as part of the proof.