Global Well-posedness and Long Time Behaviors of Chemotaxis-Fluid System Modeling Coral Fertilization

TL;DR

This paper proves the global existence, decay, and long-term mass bounds of solutions for a chemotaxis-fluid model simulating coral fertilization, advancing understanding of these biological processes.

Contribution

It establishes the first rigorous proof of global solutions and their decay properties for a complex chemotaxis-fluid system modeling coral broadcast spawning.

Findings

Global-in-time regular solutions are proven to exist.

Solutions decay over time in two and three dimensions.

Total egg and sperm masses remain positively bounded as time approaches infinity.

Abstract

We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the models as well as their temporal decays in two and three dimensions. We also show that the total masses of egg and sperm density have positive lower bounds as time tends to infinity in three dimensions.