Lower Bound of Mass in a Chemotactic Model with Advection and Absorbing Reaction

We consider a mathematical model motivated by the studies of coral broadcast spawning in spatial dimensions two and three. We establish the local and global well-posedness of regular solutions for the model. We also prove that the total mass of the egg (sperm) density asymptotically approaches a strictly positive constant, provided that the efficiency of the absorbing reaction is strong enough.