Acta Mathematica Scientia

, Volume 39, Issue 2, pp 491–497 | Cite as

Liouville Type Theorem for the Stationary Equations of Magneto-Hydrodynamics

  • Simon SchulzEmail author


We show that any smooth solution (u, H) to the stationary equations of magneto-hydrodynamics belonging to both spaces L6(ℝ3) and BMO−1(ℝ3) must be identically zero. This is an extension of previous results, all of which systematically required stronger integra-bility and the additional assumption ∇u,∇HL2(ℝ3), i.e., finite Dirichlet integral.

Key words

Liouville theorem Caccioppoli inequality Navier-Stokes equations MHD 

2010 MR Subject Classification

35B53 35Q30 76W05 


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The author wishes to thank Gui-Qiang Chen and Gregory Seregin for useful discussions.


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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