Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data

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Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion (2013, background): “Then known results say that if S(n) D(n) Cn 2 N −ε holds for some C > 0, ε > 0 and all large n, then all solutions are global in time and bounded ([16,21, 9], see also [10]), whereas if S(n) D(n) Cn 2 N +ε for some C > 0, ε > 0 and large n, then there exist solutions which blow up either in finite o”