一类三维趋化–斯托克斯方程组正则化问题解的先验估计
A Prior Estimate of Solutions to Regularization Problems of a Class of Three-Dimensional Chemotaxis-Stokes Equations
摘要: 本文研究了一类带流体耦合的三维趋化–斯托克斯方程，该模型刻画了流体环境中的生物趋化现象。大量的生物实验观测表明，在趋化流体模型中，重力对细胞运动的影响和趋化本身对流体的交互作用都应该放在方程中同时考虑。本文将在 的条件下利用权函数的方法建立正则化问题解的先验估计，为进一步研究解的定性理论做好准备。
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.
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