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This paper deals with the fully parabolic chemotaxis system of local sensingin higher dimensions. Despite the striking similarity between this system andthe Keller--Segel system, we prove the absence of finite-time blow-upphenomenon in this system even in the supercritical case. It means that for anyregular initial data, independently of the magnitude of mass, the classicalsolution exists globally in time in the higher dimensional setting. Moreover,for the exponential decaying motility case, it is established that solutionsmay blow up at infinite time for any magnitude of mass. In order to prove ourtheorem, we deal with some auxiliary identity as an evolution equation with atime dependent operator. In view of this new perspective, the directconsequence of the abstract theory is rich enough to establish global existenceof the system.

Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions