Analytical solutions to a class of non-Newtonian fluids with free boundaries

摘要

We study analytical solutions to a class of non-Newtonian fluids with free boundaries. For suitable non-Newtonian fluids, we construct a class of analytical solutions in R with both continuous density condition and the stress free condition across the free boundaries separating the fluid from vacuum. Such solutions exhibit interesting new information such as the formation of vacuum as time tends to infinitely and explicit regularities and large time decay estimates of the velocity field.