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In this note we study locally self-similar blow up for the Euler equation.The main result states that under a mild $L^p$-growth assumption on the profile$v$, namely, $\int_{|y| \sim L} |v|^p dy \lesssim L^{\g}$ for some $\g <p-2$,the self-similar solution carries a positive amount of energy up to the time ofblow-up $T$, namely, $\int_{|y| \sim L} |v|^2 dy \sim L^{N-2\a}$. The resultimplies and extends several previously known exclusion criteria. It alsosupports a general conjecture relating fractal local dimensions of the energymeasure with the rate of velocity growth at the time of possible blowup.

On the energy behavior of locally self-similar blowup for the Euler equation