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Dyadic models for ideal MHD
- Publication Year :
- 2021
-
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.<br />Comment: 20 pages
- Subjects :
- Mathematics - Analysis of PDEs
35Q35, 76B03, 76W05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2104.09440
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00021-021-00640-9