Abstract
This paper establishes the local-in-time existence and uniqueness of strong solutions in Hs for s>n/2 to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rn, n=2, 3, as well as for a related model where the advection terms are removed from the velocity equation. The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato and Ponce (1988) [13].
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1035-1056 |
| Number of pages | 22 |
| Journal | Journal of Functional Analysis |
| Volume | 267 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 15 2014 |
All Science Journal Classification (ASJC) codes
- Analysis
Keywords
- Commutator estimates
- MHD
- Magnetohydrodynamics
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Fefferman, C. L., McCormick, D. S., Robinson, J. C., & Rodrigo, J. L. (2014). Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Journal of Functional Analysis, 267(4), 1035-1056. https://doi.org/10.1016/j.jfa.2014.03.021