On the fractional chemotaxis Navier-Stokes system in the critical spaces

Abstract

<p style='text-indent:20px;'>We consider the fractional chemotaxis Navier-Stokes equations which are the fractional Keller-Segel model coupled with the Navier-Stokes fluid in the whole space, and prove the existence of global mild solutions with the small critical initial data in Besov-Morrey spaces. Our results enable us to obtain the self-similar solutions provided the initial data are homogeneous functions with small norms and considering the case of chemical attractant without degradation rate. Moreover, we show the asymptotic stability of solutions as the time goes to infinity and obtain a class of asymptotically self-similar ones.</p>

Mild solutions to the Cauchy problem for time-space fractional Keller-Segel-Navier-Stokes system

“…Jiang et.al [29] established the existence and uniqueness of global mild solution to fractional chemotaxis-Navier-Stokes system. Recently, Azevedo et.al [2] proved the existence of global mild solutions of time fractional Keller-Segel model coupled with the Navier-Stokes fluid with small critical initial data in Besov-Morrey spaces.…”