Linear stability of stratified fluids and the associated nonlinear
It's a problem that has long puzzled fluid dynamicists:
How long does it take the waves in a container of fluid to settle?
To date there is no complete mathematical analysis; the air/liquid/wall contact
line and surface tension complicate things. But for "supercritical" fluids
at high pressure (important in several industrial processes,
such as decaffeination of coffee) modeled by the incompressible
Navier-Stokes equations, the sharp distinction between liquid and vapor disappears.
Viscosity can be expected to damp internal waves with a characteristic
exponential relaxation time associated with the slowest decaying mode of the system.
This work proves that, surprisingly, there is no slowest decaying
mode in such stratified fluids. (This is a joint work with R. L. Pego and K. F. Gurski.)