Dyadic models for ideal MHD
arXiv:2104.09440 · doi:10.1007/s00021-021-00640-9
Abstract
We study two dyadic models for incompressible ideal magnetohydrodynamics, one with a uni-directional energy cascade and the other one with both forward and backward energy cascades. Global existence of weak solutions and local well-posedness are established for both models. In addition, solutions to the model with uni-directional energy cascade associated with positive initial data are shown to develop blow-up at a finite time. Moreover, a set of fixed points is found for each model. Linear instability about some particular fixed points is proved.
20 pages
References in corpus (6)
- Shell Models of Magnetohydrodynamic Turbulence
- An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
- A Blow-Up Result for Dyadic Models of the Euler Equations
- Dyadic models with intermittency dependence for the Hall MHD
- Uniqueness and non-uniqueness results for dyadic MHD models
- Blow-up of dyadic MHD models with forward energy cascade