We study the existence of global weak solutions in a three-dimensional time-dependent bounded domain for the incompressible Vlasov–Navier–Stokes system which is coupled with two convection–diffusion equations describing the air temperature and its water vapor mass fraction. This newly introduced model describes respiratory aerosols in the human aiways when one takes into account the hygroscopic effects, also inducing the presence of extra variables in the aerosol distribution function, temperature and size. The mathematical description of these phenomena leads us to make the assumption that the initial distribution of particles does not contain arbitrarily small particles. The proof is based on a regularization and approximation strategy that we solve by deriving several energy estimates, including ones with temperature and size.

中文翻译：

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与对流-扩散方程耦合的不可压缩 Vlasov-Navier-Stokes 系统弱解的全局存在

我们研究了不可压缩 Vlasov-Navier-Stokes 系统在三维时间相关有界域中的全局弱解的存在，该系统与描述气温及其水蒸气质量分数的两个对流扩散方程相耦合。当考虑到吸湿效应时，这个新引入的模型描述了人体呼吸道中的呼吸道气溶胶，还导致气溶胶分布函数、温度和大小中存在额外的变量。这些现象的数学描述使我们假设粒子的初始分布不包含任意小的粒子。证明基于正则化和近似策略，我们通过导出几个能量估计来解决，包括温度和大小的估计。