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- W3136572764 abstract "Recently, we proposed a new stochastic interpretation of the parabolic-parabolic Keller–Segel system without cut-off via a McKean–Vlasov stochastic process. The process was defined through an original type of interaction kernel which involved, in a singular way, all its past time marginal distributions. In the present paper, we study this McKean–Vlasov representation in the two-dimensional case. In this setting, there exists a possibility of a blow-up in finite time for the Keller–Segel system if some parameters of the model are large. Indeed, we prove the global in time well-posedness of the McKean–Vlasov process under some constraints involving a parameter of the model and the initial datum. Under these constraints, we also prove the global well-posedness for the Keller–Segel model in the plane." @default.
- W3136572764 created "2021-03-29" @default.
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- W3136572764 date "2021-02-01" @default.
- W3136572764 modified "2023-10-10" @default.
- W3136572764 title "A new McKean–Vlasov stochastic interpretation of the parabolic-parabolic Keller–Segel model: The two-dimensional case" @default.
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- W3136572764 doi "https://doi.org/10.1214/20-aap1594" @default.
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