Published Paper Details:

Fluid dynamics is a significant branch of applied mathematics that studies the motion of liquids and gases through mathematical models and computational techniques. The subject connects differential equations, numerical analysis, vector calculus, topology, and computational mathematics with practical applications in engineering, meteorology, medicine, astrophysics, and environmental science. This paper explores the mathematical foundations of fluid dynamics and its applications in modern mathematics. Special emphasis is placed on the Navier-Stokes equations, computational fluid dynamics (CFD), turbulence modeling, dynamical systems, and machine learning-assisted simulations. The paper also discusses current mathematical challenges, including the famous Navier-Stokes existence and smoothness problem, one of the Millennium Prize Problems. Fluid dynamics demonstrates how mathematical theories contribute directly to solving real-world scientific and engineering problems.