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Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type

Abstract

We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a system of two parabolic equations, we establish that for data which are, in a suitable sense, smaller than the diffusion parameter τ in the equation for the chemoattractant, we obtain global solutions, and for some data larger than τ , a finite time blowup. In this way, we check that our size condition for the global existence is sharp for large τ , up to a logarithmic factor.
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Dates and versions

hal-03699868 , version 1 (20-06-2022)

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Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese. Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type. 2022. ⟨hal-03699868⟩
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