Preprint B91/2016
Asymptotic Blowup Solutions in MHD Shell Model of Turbulence
Guilherme Tegoni Goedert
Keywords: turbulence | shell models | blowup | asymptotic solutions | magnetohydrodynamics

This work considers the problem of finite time singularities (blowup) in a shell
model of magnetohydrodynamic (MHD) turbulence from a dynamical sys-
tem standpoint. First, we prove a blowup criterion similar to the Beale-Kato-
Majda theorem. Further analysis is based on a renormalization scheme which
takes blowup time to infinity. This transformation associates the blowup to
an attractor of the renormalized system, found from its Poincar ?e map. This
way, we not only describe the blowup structure but also explain its universal-
ity. Following this approach, we show that, for some parameter values, the
blowup has a chaotic structure. Moreover, we observe an interesting effect
of coexisting blowup scenarios in a specific model, which are selected based
on initial conditions.