Magnetic inhibition on the Rayleigh-Taylor/thermal convection instability in non-resistive magnetohydrodynamics
The Rayleigh-Taylor (RT) instability is well known as gravity-driven instability in fluids when a heavy fluid is on top of a light one, while thermal convection instability often arises when a fluid is heated from below. Both of them appear in a wide range of applications in science and technology, such as in inertia confinement fusion, Tokamak, supernova explosions. In this talk, mathematical analysis of the magnetic RT/thermal convection instability in incompressible/compressible fluids will be presented, in particular, effects of (impressed) magnetic fields upon the growth of the RT/thermal convection instability will be discussed and analyzed quantitatively. We shall show that a sufficiently strong (impressed) magnetic field can inhibit the RT/thermal convection instability; otherwise, instability will still occur in the sense that solutions do not continuously depend on initial data.