A new upper bound for the largest growth rate of linear Rayleigh-Taylor instability

We investigate the effect of (interface) surface tensor on the linear Rayleigh-Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Lambda is proved under the instability condition (i.e., the surface tension coefficient upsilon is less than a threshold upsilon(c)) by the modified variational method of PDEs. Moreover, we find a new upper bound for Lambda. In particular, we directly observe from the upper bound that Lambda decreasingly converges to zero as upsilon goes from zero to the threshold upsilon(c).