Abstract
ABSTRACT Solutions to the chemotaxis system in a ball , , wherein and are given parameters with m−q>−1, cannot blow up in finite time provided u is uniformly-in-time bounded in for some . For radially symmetric solutions, we show that, if u is only bounded in and the technical condition is fulfilled, then, for any , there is C>0 with denoting the maximal existence time. This is essentially optimal in the sense that, if this estimate held for any , then u would already be bounded in for some .
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