Global Mild Solution for a Fractional Chemotaxis–Fluid System Modeling Coral Fertilization With Tensor‐Valued Sensitivity

ABSTRACT In this paper, we consider the following a fractional chemotaxis–fluid system modeling coral fertilization with tensor‐valued sensitivity in . Here the tensor‐valued sensitivity function satisfies . We show that if and the initial data satisfy or then this system admits a unique global mild solution, and we also determine the asymptotic behavior and optimal convergence rates of mild solution.