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- W2054734168 abstract "We consider the classical parabolic–parabolic Keller–Segel system describing chemotaxis, i.e., when both the evolution of the biological population and the chemoattractant concentration are described by a parabolic equation. We prove that when the equation is set in the whole space Rd and dimension d≥3 the critical spaces for the initial bacteria density and the chemical gradient are respectively La(Rd), a>d/2, and Ld(Rd). For in these spaces, we prove that small initial data give rise to global solutions that vanish as the heat equation for large times and that exhibit a regularizing effect of hypercontractivity type." @default.
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- W2054734168 date "2008-04-01" @default.
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- W2054734168 title "Asymptotic decay for the solutions of the parabolic–parabolic Keller–Segel chemotaxis system in critical spaces" @default.
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- W2054734168 doi "https://doi.org/10.1016/j.mcm.2007.06.005" @default.
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