A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals

Author:

Jiang Chao1,Liu Zuhan1,Lei Yuzhu1

Affiliation:

1. School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Abstract

In this paper, we considered a fractional chemotaxis fluid system with matrix-valued sensitivities and attractive–repulsive signals on a two-dimensional periodic torus T2. 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.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Jiangsu Province

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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