Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities develop during the star's explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.
Keywords: arrow of time; blast waves; fluid instabilities; interfacial mixing; nuclear synthesis; supernovae.