Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types

The uniqueness of weak solutions to the Keller–Segel systems of degenerate and singular types is proven in the class of Hölder continuous functions. Hölder continuity is expected to be an optimal regularity for weak solutions of the degenerate Keller–Segel systems under consideration. Our proof is based on the vanishing viscosity duality method.