Abstract
The decay rates of solutions to a chemotaxis-shallow water system
Highlights
We are interested in two-dimensional chemotaxis-shallow water system nt + div(nu) = Dn∆n − ∇ · (nχ(c)∇c), ct + div(cu) = Dc∆c − n f (c), ht + div(hu) = 0, (1.1)
In [14], we proved the global well-posedness of strong solution and studied the upper bound decay rates of the global solution with the initial data far from vacuum
In this paper, based on the previous works [14, 17], we are interested in the large time behavior of the global solution for the chemotaxis-shallow water system with the bacterial density n being allowed to vanish
Summary
By the Fourier splitting method, we show the first order spatial derivatives of the bacterial density tends to zero at the L2-rate (1 + t)−1. For large initial data allowing vacuum, i.e. the bacterial density n is allowed to vanish, the authors in [2] established the local existence of strong solutions and the blow-up criterion.
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