Project start: 1.10.2025.

Micropolar fluids enable a more accurate description of flow dynamics in systems where microstructural effects become significant, such as in micro- and nano-scale tubes, where classical continuum models fall short. On the other hand, real fluids are essential for modeling flows under high-pressure and high-density conditions, while ideal fluid models remain applicable in standard regimes. This research aims to integrate the micropolar framework with real fluid behavior, developing models capable of describing a wide range of physical scenarios.

The focus of the project is the development and analysis of three-dimensional flow models of micropolar fluids with cylindrical symmetry. Several key extensions are planned, including flows through non-insulated pipes (for both ideal and real fluids), models with moving walls that introduce nonhomogeneous boundary conditions, formulations of the Cauchy problem, and cases where viscosity and other parameters depend on density and/or temperature.

Each of these systems will undergo rigorous mathematical analysis, including the proof of local and global existence, uniqueness, and regularity of solutions, as well as the examination of parameter sensitivity. In parallel, convergent numerical models will be developed with integrated data-driven components. Special emphasis will be placed on advanced variants of Dynamic Mode Decomposition (DMD), which serve as approximations of the Koopman operator. Compared to traditional machine learning techniques, DMD offers better interpretability, dimensionality reduction, and the ability to identify spatio-temporal patterns at a lower computational cost. Initial testing will be conducted on simpler dynamical systems, with the goal of building robust and accurate predictive models for micropolar fluid flow.