
Mathematics 2015
A global existence result for a KellerSegel type system with supercritical initial dataAbstract: We consider a parabolicelliptic KellerSegel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in time for general subcritical ($\\rho_0\_1<8\pi$) initial data, or blowup in finite time for suitably chosen supercritical ($\\rho_0\_1>8\pi$) initial data with concentration around finitely many points. As a matter of fact there are no results claiming the existence of global solutions in the supercritical case. We solve this problem here and prove that, for a particular set of initial data which share large supercritical masses, the corresponding solution is global and uniformly bounded.
