Rayleigh-Taylor instability with heat transfer

Abstract

In this thesis, the Rayleigh-Taylor instability effect with heat transfer in the setting of the Navier-Stokes equations, given three-dimensional and incompressible fluids, is investigated. Under suitable initial and boundary conditions, the existence of the temperature variable in the weak form is established by the Galerkin Method; the uniqueness of the solution can be proved by energy estimates, and furthermore, if more conditions on the coefficients are imposed, it can be demonstrated that the temperature belongs to some H ̈older continuous class. By the regularity result above, a positive minimum temperature result can be established. As demonstrated by F. Jiang and S. Jiang, given Rayleigh-Taylor instability driven initial conditions, the exponential growth effect can be shown for the density and the velocity in the fully nonlinear setting; thus, the instability for the temperature in the sense of Hadamard can be proved.