MATHEMATICAL APPROACHES TO FLUID DYNAMICS: MODELS, METHODS, AND APPLICATIONS

Fluid dynamics is a central area of applied mathematics with significant implications for physics, engineering, and environmental sciences. The study of fluid motion through mathematical models enables the prediction and optimization of systems ranging from industrial pipelines to atmospheric circulation. This paper provides an overview of mathematical foundations in fluid dynamics, including the governing equations, analytical and numerical techniques, and modern applications. The review highlights classical formulations such as the Euler and Navier–Stokes equations, advances in computational fluid dynamics (CFD), and their interdisciplinary impact. Emphasis is placed on the mathematical challenges underlying turbulence, stability analysis, and boundarylayer phenomena.