Abstract
This paper deals with the following chemotaxis system: in a bounded domain with smooth boundary under no-flux boundary conditions, where satisfies for all with l⩾2 and some nondecreasing function on [0,∞). Here, f(v)∈C1([0,∞)) is nonnegative for all v⩾0. It is proved that when , the system possesses at least one global bounded weak solution for any sufficiently smooth nonnegative initial data. This extends a recent result by Wang (Math. Methods Appl. Sci. 2016 39: 1159–1175) which shows global existence and boundedness of weak solutions under the condition . Copyright © 2017 John Wiley & Sons, Ltd.
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