The two-dimensional Keller-Segel model after blow-up

By Jean Dolbeault, Christian Schmeiser. 2009

77 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/57e2d71969b11adc6603f8a462aed11591a72e05

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In Applied Mathematics

In Modeling and Simulation

In Molecular Biology

Citations in the corpus

Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, methodology): “1) in the sense of Poupaud’s weak solutions [60], which make sense even if there are mass concentrations, have been constructed by Dolbeault and Schmeiser in [31] by taking sequences of regularized problems and extracting a measure for u(t) along with an appropriate ‘defect measure’ to make sense of”
Nondegeneracy of blow-up points for the parabolic Keller–Segel system (2014, background): “Finally, let us mention that the question of the continuation of solutions after blow-up for Γ = 0, with persistence of moving Dirac masses, has also been studied (see [13,30,49] and the references therein).”
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) in the sense of Poupaud’s weak solutions [60], which make sense even if there are mass concentrations, have been constructed by Dolbeault and Schmeiser in [31] by taking sequences of regularized problems and extracting a measure for u(t) along with 3”
Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model (2010, background): “ the t→ ∞ limit of any such solution is a Dirac mass 8πat the center of mass of the initial data. Furthermore, a point mass of mass Mis a stationary measure-valued solution in the sense introduced in [22] if and only if M≥ 8π. Let us ﬁnally mention that an analysis of basins of attraction of λ in th”