2022/02/28 by Fei Jiang, Song Jiang, Jiang, Fei +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35M11 #msc:76E25 #msc:76W05
paper · pdf · doi:10.48550/arxiv.2202.13731
56. arXiv admin note: text overlap with arXiv:2105.06472
arxiv created 2022/02/28 · arxiv updated 2022/03/01
It is still open whether the phenomenon of inhibition of Rayleigh--Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive viscous magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly proved in the linearized case by Wang in \citeWYC. In this paper, we prove such inhibition phenomenon by the (nonlinear) inhomogeneous, incompressible, viscous case with Navier (slip) boundary condition. More precisely, we show that there is a critical number of field strength m_\mmC, such that if the strength |m| of a horizontal magnetic field is bigger than m_\mmC, then the small perturbation solution around the magnetic RT equilibrium state is algebraically stable in time. In addition, we also provide a nonlinear instability result for the case |m|∈[0, m_\mmC). The instability result presents that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small.