Weak Solutions to a Parabolic-Elliptic System of Chemotaxis

By T. Senba, Takashi Suzuki. 2002

119 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Cell Biology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/9b7f6c49f0d775073603ec6fcef028064232393f

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Citations in the corpus

Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$R2 with Measure-Valued Initial Data (2012, background): “Senba and Suzuki [63] construct weak solutions only under the assumption maxx∈R2 µ({x}) 8π, however, their solutions are not a priori mild solutions and it is far from clear that more general solutions would necessarily agree with the mild solution.”
The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane (2006, background): “Unfortunately, we have no proof for this fact but the following result seems to indicate that the stability of the constant function 8π could be a rather delicate issue.”
Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, background): “Senba and Suzuki [63] construct weak solutions only under the assumption maxx∈R2 μ({x}) 8π , however, their solutions are not a priori mild solutions and it is far from clear that more general solutions would necessarily agree with the mild solution.”
The drift–diffusion system in two-dimensional critical Hardy space (2008, unknown): “[1,28,29,41–44,46,47,51–53,56]).”
The $8\pi$-problem for radially symmetric solutions of a chemotaxis model in a disc (2006, background): “Other approaches allowing to consider measures as initial data have been developed in [18, 10, 3, 4, 5].”
Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2 (2007, methodology): “using the symmetry in x, y for the concentration gradient was introduced in [ 46 ].”
PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic (2004, background): “moment), as it is suggested in two dimensions and for radial solutions by the result of [32] (see also [ 60 ]).”
Optimal critical mass in the two dimensional Keller–Segel model in R2 (2004, background): “Le cas général est moins connu (voir [6, 17] pour des concentrations, [13] pour des calculs numériques).”