A Prior Estimate of Solutions to Regularization Problems of a Class of Three-Dimensional Chemotaxis-Stokes Equations

Abstract

In this paper, we study a class of three-dimensional chemotaxis-Stokes equations with fluid cou-pling, which describes the phenomenon of chemotaxis in the fluid environment. Numerous bio-logical experimental observations have shown that both the effect of gravity on bacterial motility and the interaction of chemotaxis itself on the fluid should be placed in the equations for simulta-neous consideration in the chemotaxis fluid model. In this paper, we will establish a prior estimate of the solution of the regularization problem under the condition of by using the method of weight function, in order to prepare for the further study of the qualitative theory of the solution.