The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
We consider the dynamics of two layers of incompressible electrically conducting fluid interacting with the magnetic field, which are confined within a 3D horizontally infinite slab and separated by a free internal interface. We assume that the upper fluid is heavier than the lower fluid so that the fluids are susceptible to the Rayleigh-Taylor instability. Yet, we show that the viscous and non-resistive problem around the equilibrium is nonlinearly stable provided that the strength of the vertical component of the steady magnetic field, \abs{\bar B_3}$\abs{\bar B_3}$ , is greater than the critical value, \mathcal{M}_c , which we identify explicitly. We also prove that the problem is nonlinearly unstable if \abs{\bar B_3}<\mathcal{M}_c . Our results indicate that the non-horizontal magnetic field has strong stabilizing effect on the Rayleigh-Taylor instability but the horizontal one does not have.
Biography:
Professor Yanjing Wang holds his PhD from Xiamen University in 2011. Now he is a professor of School of Mathematical Sciences in Xiamen University. His research interests are nonlinear partial differential equations arising from fluid dynamics and kinetic theory, especially Navier-Stokes equations and Boltzmann equation.