Existence and uniqueness of mild solutions to the chemotaxis-fluid system modeling coral fertilization

Abstract

Abstract In this paper, we consider the egg-sperm chemotaxis model of coral with the incompressible fluid equations in the whole space. The existence of global mild solutions in scaling invariant spaces is proved with sufficient small initial data. Here the main tool we use is the implicit function theorem. Furthermore, we obtain the asymptotic stability of solutions when the time goes to infinity. Since the initial data could be in the weak L p $L^{p}$ -spaces, we finally get the existence of self-similar solutions when the initial data are small homogeneous functions.

Keywords

• Chemotaxis-fluid system
• Existence and uniqueness
• Mild solutions
• Self-similar solutions
• Implicit function theorem