Keller–Segel–Stokes interaction involving signal‐dependent motilities

<jats:p>The chemotaxis‐Stokes system <jats:disp-formula> </jats:disp-formula>is considered along with homogeneous boundary conditions of no‐flux type for and , and of Dirichlet type for , in a smoothly bounded domain . Under the assumption that , that is bounded on each of the intervals with arbitrary , and that with some and , we have <jats:disp-formula> </jats:disp-formula>It is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.</jats:p>