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The aim of this paper is to establish Liouville type results for the stationary MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero. Moreover, we also obtain Liouville type theorem for the case of axially symmetric MHD equations. Our results generalize previous works by Schulz \cite{Sc2018} and Seregin-Wang \cite{SW2018}.
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참고문헌 (19)
참고문헌 신청
Shangkun Weng / 2016 / Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations / Discrete and Continuous Dynamical Systems 36(10):5267~5285
Dongho Chae / 2016 / On Liouville type theorems for the steady Navier-Stokes equations in R3 / Journal of Differential Equations 261(10):5541~5560
P. A. Davidson / 2001 / An Introduction to Magnetohydrodynamics, Cambridge Texts in Ap-plied Mathematics / Cambridge University Press
G. P. Galdi / 2011 / An introduction to the mathematical theory of the Navier-Stokes equations, Springer Monographs in Mathematics / Springer
M. Giaquinta / 1983 / Multiple integrals in the calculus of variations and nonlinear elliptic systems / Annals of Mathematics Studies 105
Dongho Chae / 2016 / On Liouville type theorems for the steady Navier-Stokes equations in R3 / Journal of Differential Equations 261(10):5541~5560
P. A. Davidson / 2001 / An Introduction to Magnetohydrodynamics, Cambridge Texts in Ap-plied Mathematics / Cambridge University Press
G. P. Galdi / 2011 / An introduction to the mathematical theory of the Navier-Stokes equations, Springer Monographs in Mathematics / Springer
M. Giaquinta / 1983 / Multiple integrals in the calculus of variations and nonlinear elliptic systems / Annals of Mathematics Studies 105
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