Regularizing effect of the forward energy cascade in the inviscid dyadic model

Cheskidov, Alexey; Zaya, Karen

doi:10.1090/proc/12494

Regularizing effect of the forward energy cascade in the inviscid dyadic model
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by Alexey Cheskidov and Karen Zaya PDF

Proc. Amer. Math. Soc. 144 (2016), 73-85 Request permission

Abstract:

We study the inviscid dyadic model of the Euler equations and prove some regularizing properties of the nonlinear term that occur due to forward energy cascade. We show every solution must have $\frac {3}{5}$ $L^2$-based (or $\frac {1}{10}$ $L^3$-based) regularity for all positive time. We conjecture this holds up to Onsager’s scaling, where the $L^2$-based exponent is $\frac {5}{6}$ and the $L^3$-based exponent is $\frac {1}{3}$.

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