Abstract
The main purpose of this paper is to study the global existence of large-data solutions to the following chemotactic model with general rotational sensitivity caused by two stimuli: ut=Δu−∇⋅(uS1(x,u,v,w)∇v)+∇⋅(uS2(x,u,v,w)∇w),vt=Δv−uv,wt=Δw−uwin a bounded domain Ω⊂Rn with smooth boundary under suitable initial–boundary conditions. Systems of this type arise in mathematical biology as models for the evolution of Escherichia coli suspensions in a vertical cylindrical cell by letting the bacteria be uniformly distributed in an oxygen-saturated medium with a glucose concentration step gradient at the mid height of the cell.For the two-dimensional case, the first author and Li (2016) showed that for suitably regular initial data (u0,v0,w0) fulfilling a smallness condition on the L∞-norm of v0 and w0, the initial–boundary value problem of this system possesses a global bounded classical solution.In this paper, we will remove such a smallness assumption to show the global existence of generalized solutions with general large initial data by using a new method developed by Winkler (2015). Our result holds in arbitrary dimension n≥1.
Published Version
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