Uniqueness and continuity of solution for the initial data in the scaling invariant class of the degenerate Keller-Segel system

We consider the degenerate Keller-Segel system (KS)(m) below. We find the functional space L-s(0, T; L-p(R-N)) with some p, s for the uniqueness and continuity of weak solutions with respect to the initial data. Our space is discussed from a viewpoint of the scaling invariant class associated with (KS)(m) for gamma = 0. The technique is based on the L-1-contraction principle for the porous medium equation.