English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate the stabilizing effects of the magnetic fields in thelinearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneousincompressible viscous magnetohydrodynamic fluid of zero resistivity in thepresence of a uniform gravitational field in a three-dimensional boundeddomain, in which the velocity of the fluid is non-slip on the boundary. Byadapting a modified variational method and careful deriving \emph{a priori}estimates, we establish a criterion for the instability/stability of thelinearized problem around a magnetic RT equilibrium state. In the criterion, wefind a new phenomenon that a sufficiently strong horizontal magnetic field hasthe same stabilizing effect as that of the vertical magnetic field on growth ofthe magnetic RT instability. In addition, we further study the correspondingcompressible case, i.e., the Parker (or magnetic buoyancy) problem, for whichthe strength of a horizontal magnetic field decreases with height, and alsoshow the stabilizing effect of a sufficiently large magnetic field.

On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics