LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

doi:10.1007/s10473-019-0213-7

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

LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

Simon SCHULZ

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

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/Abstract

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, ▽H ∈ L²(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, ▽H ∈ L²(R³), i.e., finite Dirichlet integral.

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

Simon SCHULZ. LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS[J]. 数学物理学报(英文版), 2019, 39(2): 491-497.

Simon SCHULZ. LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS[J]. Acta mathematica scientia,Series B, 2019, 39(2): 491-497.

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LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

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