Global classical solutions to two-dimensional chemotaxis-shallow water system

Abstract

<p style='text-indent:20px;'>We consider the Cauchy problem of two-dimensional chemotaxis-shallow water system in the present paper. For regular initial data with small energy but possibly large oscillations, we prove the global well-posedness of classical solution. Then, we show the large-time behavior of the solution using the time-independent lower-order estimates as well.