We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form

where \(\kappa \ge 0\), \(\mu >0\) and, in contrast to the commonly investigated variants of chemotaxis-fluid systems, the signal concentration on the boundary of the domain \(\Omega \subset \mathbb {R}^N\) with \(N\in \{2,3\}\) is a prescribed time-independent nonnegative function \(c_*\in C^{2}\!\left( {{\,\mathrm{\overline{\Omega }}\,}}\right) \). Making use of the boundedness information entailed by the quadratic decay term of the first equation, we will show that the system above has at least one global weak solution for any suitably regular triplet of initial data.

我们研究了一个趋化-斯托克斯系统，其信号消耗和逻辑源项的形式为

其中\(\kappa \ge 0\) , \(\mu >0\)与通常研究的趋化流体系统变体相比，域边界上的信号浓度\(\Omega \subset \ mathbb {R}^N\)与\(N\in \{2,3\}\)是一个规定的时间无关的非负函数\(c_*\in C^{2}\!\left( {{\ ,\mathrm{\overline{\Omega }}\,}}\right) \)。利用第一个方程的二次衰减项所包含的有界信息，我们将证明上述系统对于任何合适的初始数据三元组至少有一个全局弱解。