Global solutions and large time behavior for the chemotaxis-shallow water system (Q828295)

The authors study a chemotaxis system coupled with the viscous shallow water equations which models bacteriae chemotactic movement towards higher concentration of oxygen they consume, under gravitational potential and convective transport effects. A well-posedness result is proved for that two-dimensional evolution problem with small initial data in the critical Besov spaces. Time decay of solutions -- coinciding with that for the diffusion asymptotics -- is proved.