We consider an improved Nernst–Planck–Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non-equilibrium. The elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, is taken into account. The model consists of convection–diffusion–reaction equations for the constituents of the mixture, of the Navier–Stokes equation for the barycentric velocity and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross-diffusion phenomena must occur, and the mobility matrix (Onsager matrix) has a non-trivial kernel. In this paper, we establish the existence of a global-in-time weak solution, allowing for a general structure of the mobility tensor and for chemical reactions with fast nonlinear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time.

我们考虑由Dreyer等人首先提出的改进的Nernst-Planck-Poisson模型。在2013年用于非平衡态的可压缩等温电解质。考虑到介质的弹性变形，该变形引起质量和动量传输的固有耦合。该模型包括混合物的对流扩散反应方程式，重心速度的Navier-Stokes方程和电位的Poisson方程。由于质量守恒的原理，必须发生交叉扩散现象，并且迁移率矩阵（Onsager矩阵）具有不平凡的核。在本文中，我们建立了全局及时弱解决方案的存在，考虑到迁移张量的一般结构以及在主体和活动边界上具有快速非线性速率的化学反应。我们表征了系统的奇异状态，表明该化学物种只能在空间中全局消失，并且该现象必须集中在时间为零的紧凑度量集中。