Fluid Mechanics and Navier-Stokes Equations

Abstract

Navier-Stokes differential equations constitute the most prominent mathematical model for explaining and describing the behavior of fluids. These equations found the basis of fluid mechanics and have countless applications in numerous fields. Besides their wide applications, the problem of existence and smoothness of solutions of Navier-Stokes equations, remains of the most challenging open problem of mathematics. Regarding the practical and scientific significance of these equations, this thesis discusses the details of derivation of Navier-Stokes equations and other related issues of fluid mechanics. Furthermore, some of the key mathematical theorems and techniques used for derivation and analysis of Navier-Stokes equations are explained and reviewed.ÖZ: Navier-Stokes diferansiyel denklemleri akışkanlar mekaniği için çok önemlidir ve birçok farklı alanda uygulamalara sahiptir. Bu denklemler akışkanların hareketini açıklamaktadır. Bu tez, akışkanların temel mekaniklerini incelemekte ve Navier-Stokes diferansiyel denklemlerini ele almaktadır.