Nonlinear Rayleigh-Taylor instability of inhomogeneous incompressible geophysical fluids with partial dissipation

This article examines the Rayleigh-Taylor instability in an rotating inhomogeneous, incompressible fluid with partial viscosity. First, using the modified variational method, we demonstrate the existence of an exponentially growing normal mode in H k , k ⩾ 0 and establish the instability of the linearised problem. Then, we obtain a nonlinear energy estimate for the problem with small initial data. In this process, we employ an innovative method to derive energy estimates for both density and velocity, effectively addressing the challenges posed by partial viscosity. Third, we prove the existence of a classical solution for H³ initial data, provided it satisfies a compatibility condition. Finally, by integrating the results of the previous steps, we establish the nonlinear instability of the system in the Hadamard sense.