The project investigates the mathematical foundations of fluid mechanics, focusing on the limitations of

classical models, such as the Euler and Navier-Stokes equations, in real-world applications. Recent

discoveries, such as the existence of infinitely many low-regularity solutions, reveal pathological

behaviors that undermine the predictive reliability of these models. Therefore, the research considers

complex factors, such as electric fields, capillary effects, vortices, and phase transitions, going beyond

traditional theoretical frameworks. One of the key objectives is to establish rigorous connections between

different models describing the same phenomena at various scales. This approach aims to address

challenges related to nonlinear systems and deepen the theoretical understanding of fluid dynamics. The

research findings will also provide insights into related areas, such as biological systems, which

conceptually resemble fluid mechanics.