| Summary: | In this paper, we considered a fractional chemotaxis fluid system with matrix-valued sensitivities and attractive–repulsive signals on a two-dimensional periodic torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mn>2</mn></msup></semantics></math></inline-formula>. This model describes the interaction between a type of cell that proliferates following a logistic law, and the diffusion of cells is fractional Laplace diffusion. The cells and attractive–repulsive signals are transported by a viscous incompressible fluid under the influence of a force due to the aggregation of cells. We proved the existence and uniqueness of the global classical solution on the matrix-valued sensitivities, and the initial data satisfied the regular conditions. Moreover, by using energy functionals, the stabilization of global bounded solutions of the system was proven.
|
|---|