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- W2897734974 abstract "Motivated by an equation arising in magnetohydrodynamics, we address the well-posedness theroy for the non-diffusive magneto-geostrophic equation. Namely, an active scalar equation in which the divergence-free drift velocity is one derivative more singular that the active scalar. In cite{Friedlander-Vicol_3}, the authors prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces, but locally well posed in spaces of analytic functions. Here, we give an example of a steady state that is nonlinearly stable for periodic perturbations with initial data localized in frequency straight lines crossing the origin. For such well-prepared data, the local existence and uniqueness of solutions can be obtained in Sobolev spaces and the global existence holds under a size condition over the $H^{5/2^{+}}(mathbb{T}^3)$ norm of the perturbation." @default.
- W2897734974 created "2018-10-26" @default.
- W2897734974 creator A5089509479 @default.
- W2897734974 date "2018-10-19" @default.
- W2897734974 modified "2023-09-27" @default.
- W2897734974 title "On the non-diffusive Magneto-Geostrophic equation." @default.
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