In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.
In this paper, Lie point symmetry group of the Harry-Dym type equation with Riemann-Liouville fractional derivative is constructed. Then complete subgroup classification is obtained by means of the optimal system method. Finally, corresponding group-invariant solutions with reduced fractional ordinary differential equations are presented via similarity reductions.
