A Short Review on the Analytical Methods in Fluid Dynamics Research: The Importance of Exact Solutions

The main objective of this review is to report on key mathematical issues related to the analytical methods of the Navier-Stokes equations, especially the attempt of generating exact solution. Several aspects of exact solutions to provide mathematical justifications are criticised. In particular, some elementary functions appear in exact solutions are sometime found to have difficulties describing the actual phenomena. For example, in boundary layer flows, the difference from the outer layer is hard to accommodate. Additional matched function usually implemented to grasp the whole picture. In some conditions even, the situation is more obscure such that the considered problem approaching singularity. Turbulent flows is also reviewed both in physical and mathematical point of view. Since main structures of turbulent flows can be seen as consequences of the dynamics of the Navier-Stokes equations, resolving turbulence should be put as a main goal of analytical research.