Existence, uniqueness and decay estimates on mild solution to a fractional chemotaxis-fluid system

Kerui Jiang, Zhi Ling, Zuhan Liu, Ling Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2020.029

Abstract


We investigate a fractional chemotaxis system coupled with the Navier-Stokes fluid in the whole space $\mathbb{R}^{N}$ with $N\geq 3$. With the help an appropriate functional space, we develop a framework for a \textit{unified} treatment of the existence, uniqueness and decay estimates of global mild solutions to this problem under the assumption that initial data are small enough.

Keywords


Fractional chemotaxis; fractional Navier-Stokes; global mild solution; decay estimates

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