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Well-posedness for two types of generalized Keller-Segel system of chemotaxis in critical Besov spaces

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  • In this paper, we study two types of generalized Keller-Segel system of chemotaxis. We establish the global existence and uniqueness of solutions to the semilinear Keller-Segel system of doubly parabolic type and the nonlinear nonlocal type Keller-Segel system with data in Besov spaces. Moreover, we prove the stability of solution to the first type. Our main tools are the $L^p-L^q$ estimates for $e^{-t(-\triangle)^{\theta/2}}$ in Besov spaces and the perturbation of linearization.
    Mathematics Subject Classification: Primary: 35K55, 35K15; Secondary: 92C17, 92B05.


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