Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems

By Yoshie Sugiyama. Differential and Integral Equations, 2006

175 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7e4b761417d0028f46f5d3f3fb90277fbf6afbb9

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Citations in the corpus

On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (2011, background): “(32) This difference of balance was studied to obtain Theorem 13 (First criticality, [54, 55]).”
Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions (2008, methodology): “This criterion improves over the results in [30, 31] since it is only based on the boundedness or unboundedness in time of the L-norm of the solutions and it has to be compared to a similar criterion based on the logarithmic entropy in the classical PKS system in two dimensions obtained in [3].”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, unknown): “2) when Ω is the whole space R and f(u, v) = 0 (see [8],[17] [28], [36], [35]).”
Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime (2020, background): “We indicate to the reader [4, 31], where one can find the analysis concerning the local-in-time existence of weak solutions to problem (1) for a = b = 0 and m > 2 − 2 n , as well as [3] where for a = b = m = 1 and η = α the same question is addressed for strong solutions.”
Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$R2 with Measure-Valued Initial Data (2012, background): “1) involving nonlinear diffusion which are critical in higher dimensions have also been studied [51, 14, 65, 66, 10, 50] (see also the related [53]).”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, background): “Moreover, in the case of the Newtonian or Bessel potential, m = 2 − 2/d and the critical diffusion exponent of the PKS models discussed in [13, 57, 58] is recovered.”
Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, background): “1) involving nonlinear diffusion which are critical in higher dimensions have also been studied [10,14,50,51,65,66] (see also the related [53]).”
Equilibria of homogeneous functionals in the fair-competition regime (2016, background): “For the Newtonian case, global existence vs blow-up of weak solutions has been investigated for the diffusion coefficients m = 1 [30], 1 < m ≤ 2− 2 N [49,52], m = 2N N+2 [26], 2N N+2 < m < 2− 2 N [27,39] and for the whole range 0 < m ≤ 2 − 2 N [4].”