具有Dirichlet信号边界的一类趋化–流体模型的研究
Study on a Chemotaxis-Fluid Model with Dirichlet Signal Boundary
摘要: 本文讨论一类具有规定信号浓度的趋化–流体耦合方程组解的性质。利用二维有界区域上的插值不等式和边界上的逐点不等式，得到细胞密度和化学信号浓度梯度的联合估计，并结合算子半群理论，最终证得该方程组的初边值问题存在整体有界的经典解。
Abstract: In this paper, the properties of solutions to the chemotaxis-fluid system with prescribed signal con-centration on the boundary are considered. By using the interpolation inequality in a two- dimen-sional bounded domain and a pointwise inequality on the boundary, the joint estimates to cell den-sity and chemical signal concentration gradient are obtained, and combined with the operator semigroup theory, it is shown that the initial boundary value problem of the chemotaxis-fluid sys-tem exists a global and bounded classical solution.
文章引用：况旺, 侯智博. 具有Dirichlet信号边界的一类趋化–流体模型的研究[J]. 应用数学进展, 2024, 13(2): 730-737. https://doi.org/10.12677/AAM.2024.132071

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