On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces

Abstract : We investigate the existence and uniqueness issues of the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical regularity spaces. First, we establish a global result for small initial data in the Besov spacesḂ 3 p −1 p,1 with 1 ≤ p < ∞, and the conservation of higher regularity. Second, in the case where the viscosity is equal to the magnetic resistivity, we obtain the global well-posedness for (small) initial data in the larger critical Besov spaces of typeḂ 1 2 2,r for any r ≥ 1. In the particular case r = 1, we also establish the local existence for large data, and supplement our results with continuation criteria. To the best of our knowledge, the present paper is the first one where well-posedness is proved for the Hall-MHD system, in a critical regularity setting.
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Contributor : Raphaël Danchin <>
Submitted on : Thursday, November 7, 2019 - 11:22:46 AM
Last modification on : Saturday, November 9, 2019 - 1:27:08 AM


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  • HAL Id : hal-02353221, version 1
  • ARXIV : 1911.03246



Raphaël Danchin, Jin Tan. On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces. 2019. ⟨hal-02353221⟩



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