On the energy behavior of locally self-similar blowup for the Euler equation Anne BronziRoman Shvydkoy Primary:76B03Secondary:35Q31Euler equationself-similar solutions In this note, we study locally self-similar blowup for the Euler equation. The main result states that under a mild $L^p$-growth assumption on the profile $v$, namely $\displaystyle\int_{|y|\sim L}|v|^p\,\mathrm{d}y\lesssim L^{\gamma}$ for some $\gamma<p-2$, the self-similar solution carries a positive amount of energy up to the time of blowup $T$, namely, $\displaystyle\int_{|y|\sim L}|v|^2\,\mathrm{d}y\sim L^{N-2\alpha}$. The result implies and extends several previously known exclusion criteria. It also supports a general conjecture relating fractal local dimensions of the energy measure with the rate of velocity growth at the time of possible blowup. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5657 10.1512/iumj.2015.64.5657 en Indiana Univ. Math. J. 64 (2015) 1291 - 1302 state-of-the-art mathematics http://iumj.org/access/