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Global Stability of Keller--Segel Systems in Critical Lebesgue Spaces


Academic Report

Title: Global Stability of Keller--Segel Systems in Critical Lebesgue Spaces

Reporter: JIANG Jie, Associate Research Fellow (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)

Time: July16, 2018 (Monday) PM 15:00-16:00

Location:A1101# room, Innovation Park Building

Contact: YU Fang (tel:84708351-8025)


Abstract: In this talk, we present some recent results on global stability for classical Keller—Segel system of chemotaxis. We will first talk about some related results for the Keller—Segel model, including global boundedness and blow-up results. Then we discuss the stability problem of Keller—Segel equation near spatially homogeneous steady solutions which is an open problem proposed in a recent survey by N. Bellomo et al. By establishing certain delicate L^p-L^q decay estimates for the associated linearized semigroup, we give a partially affirmative answer to the problem. More importantly, our results indicate that nontrivial globally bounded classical solution exists with any given large total mass provided the domain is sufficiently large. This is the first evidence with rigorous proof for the existence of nontrivial global classical solution with Large total mass.

The brief introduction to the reporter:  Jiang Jie, Associate Research Fellow of Wuhan Institute of physics and mathematics, Chinese Academy of Sciences. He received his doctorate in science from the school of Mathematical Sciences of Fudan University in 2009, and his tutor is Professor Zheng Songmu. From 2009 to 2011, he worked as a postdoctoral fellow under the guidance of academician Guo Bailing in Institute of Applied Physics and computational mathematics of Beijing. The main research fields are the multi class nonlinear evolution equations, such as phase field fluid equations, chemokine equations and so on. The existence and uniqueness, the boundedness, the asymptotic behavior and the equilibrium state of the global solution and the properties of the infinite dimensional dynamic system.