Global existence and uniqueness of mild solution for a fractional Keller-Segel system in Besov-Morrey spaces
DOI: https://doi.org/10.3846/mma.2025.23324Abstract
This paper investigates the fractional Keller-Segel system involving both temporal and spatial variables. We examine fractional dissipation mechanisms for the physical variables, including chemotactic diffusion with fractional dissipation, and incorporate a time-fractional variation in the Caputo sense. Our analysis centers on the fractional heat semigroup, deriving time-decay and integral estimates for Mittag-Leffler operators in Besov-Morrey spaces. Furthermore, we establish a bilinear estimate arising from the nonlinearity of the Keller-Segel system, avoiding reliance on auxiliary norms. These results are then employed to demonstrate the existence and uniqueness of mild solution in Besov-Morrey spaces.
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existence and uniqueness of mild solution, Mittag-Leffler operators, Besov-Morrey spaces, Caputo sense, fractional systemHow to Cite
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Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.