A Blow-Up Result for Dyadic Models of the Euler Equations

TL;DR

This paper demonstrates that certain dyadic models of the Euler equations experience finite-time blow-up in specific Sobolev norms, advancing understanding of singularity formation in fluid dynamics models.

Contribution

It establishes a new blow-up result for generalized dyadic Euler models, partially answering an open question and unifying previous findings.

Findings

Blow-up occurs in the $H^{1/3+ ext{delta}}$-norm for the model.

Recover previous blow-up results as corollaries.

Provides insights into singularity formation in dyadic Euler models.

Abstract

We partially answer a question raised by Kiselev and Zlatos in \cite{MR2180809}; in the generalized dyadic model of the Euler equation, a blow-up of $H^{1/3+\delta}$-norm occurs. We recover a few previous blow-up results for various related dyadic models as corollaries.