Ill-Posedness of the Kelvin–Helmholtz Problem for Incompressible MHD Fluids
Abstract. In this paper, under violation of the Syrovatskij stability condition, we prove the ill-posedness of the well-known Kelvin–Helmholtz problem of incompressible ideal magnetohydrodynamics (MHD) equations. This result underscores the stabilizing role of magnetic fields satisfying the Syrovatskij condition .
Authors
- Zhao Bin (ORCID: https://orcid.org/0000-0002-9689-3186)
- Binqiang Xie (ORCID: https://orcid.org/0000-0002-1569-3458)
- DaiWen HUANG
Institutions
- Institute of Applied Physics (UA)
- Guangdong University of Technology (CN)
- Institute of Applied Physics and Computational Mathematics (CN)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2026-10-14
- DOI
- https://doi.org/10.1137/25m1777025
- Primary Topic
- Navier-Stokes equation solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- China Postdoctoral Science Foundation
- Chinese University of Hong Kong