Critical space for the parabolic-parabolic Keller–Segel model in Rd

61 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension (2010, background): “One available criterion for global existence involves the L−norm of the initial cell density [18, 19, 20, 36].”
The parabolic-parabolic Keller-Segel model in R2 (2008, background): “Indeed, in [11, 12, 13] the authors proved the global existence of weak solution of system (PKS) of parabolic-parabolic, parabolic-elliptic and parabolic degenerate type under a smallness condition on ‖n0‖Ld/2 .”
Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller--Segel equations in the whole space (2013, unknown): “Thus, Proposition 3 is proved.”
Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces (2009, background): “[8] L. Corrias, B. Perthame, Asymptotic decay for the solutions of the parabolic–parabolic Keller–Segel chemotaxis in critical spaces, Math.”
A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, background): “The Keller–Segel system in higher space dimensions has been investigated in [13,14] and for the system with nonlinear diffusion to prevent blow-up, results can be found in [9, 24].”