Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model

For the Patlak–Keller–Segel problem with critical power m = 2 − 2/d, we prove that all radial solutions with critical mass would converge to a family of stationary solutions, while

The very well-known dichotomy arising in the behavior of the macroscopic Keller–Segel system is derived at the kinetic level, being closer to microscopic features. Indeed, under

Degenerate parabolic system, chemotaxis, Keller-Segel model, drift term, decay property, asymptotic behavior, Fujita exponent, porous medium equation, Barenblatt solution..

The crucial question to be addressed concerns the interpretation of the dS/AdS UIR’s (or quantum AdS and dS elementary systems) from a (asymptotically) minkowskian point of view..

Theorem 1.8. This paper is some kind of adaptation of the work of Fournier- Hauray-Mischler in [9] where they show the propagation of chaos of some particle system for the 2D

– Super-critical case: M > M c , we prove that there exist solutions, corresponding to initial data with negative free energy, blowing up in finite time, see Proposition

Indeed, under the assumption of spherical symmetry, we prove that solutions with initial data of large mass blow-up in finite time, whereas solutions with initial data of small mass

Keller-Segel model, Existence, Weak solutions, Free energy, Entropy method, logarithmic Hardy-Littlewood-Sobolev inequality, Critical Mass, Aubin-Lions compactness