Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity |
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Affiliation: | School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China;Institute for Applied Mathematics, School of Mathematics, Southeast University, Nanjing 211189,PR China;School of Mathematics and Statistics Science, Ludong University, Yantai 264025, PR China |
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Abstract: | In this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates. |
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Keywords: | Fractional chemotaxis Energy method Global classical solution Decay estimates |
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