数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 491-497.doi: 10.1007/s10473-019-0213-7

• 论文 • 上一篇    下一篇

LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

Simon SCHULZ   

  1. Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, Oxford, United Kingdom
  • 收稿日期:2018-02-06 修回日期:2018-10-15 出版日期:2019-04-25 发布日期:2019-05-06
  • 作者简介:Simon SCHULZ,simon.schulz1@maths.ox.ac.uk
  • 基金资助:
    The author is supported by the Engineering and Physical Sciences Research Council[EP/L015811/1].

LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

Simon SCHULZ   

  1. Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, Oxford, United Kingdom
  • Received:2018-02-06 Revised:2018-10-15 Online:2019-04-25 Published:2019-05-06
  • Supported by:
    The author is supported by the Engineering and Physical Sciences Research Council[EP/L015811/1].

摘要: We show that any smooth solution (u, H) to the stationary equations of magnetohydrodynamics 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 integrability and the additional assumption ▽u, ▽HL2(R3), i.e., finite Dirichlet integral.

关键词: Liouville theorem, Caccioppoli inequality, Navier-Stokes equations, MHD

Abstract: We show that any smooth solution (u, H) to the stationary equations of magnetohydrodynamics 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 integrability and the additional assumption ▽u, ▽HL2(R3), i.e., finite Dirichlet integral.

Key words: Liouville theorem, Caccioppoli inequality, Navier-Stokes equations, MHD