## Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis.(English)Zbl 0901.35104

The Keller-Segel system (KS), a mathematical model describing aggregation of cellular slime models, is studied. In particular, the time global existence and $$L^\infty$$ estimate of the solution of (KS) in a bounded domain $$\Omega \subset \mathbb{R}^2$$ with smooth boundary $$\partial \Omega$$ is examined by using the Trudinger-Moser inequality extended to the Sobolev space $$W^{1,p} (\Omega)$$.
Reviewer: S.Totaro (Firenze)

### MSC:

 35Q80 Applications of PDE in areas other than physics (MSC2000) 46N20 Applications of functional analysis to differential and integral equations