Current Updates in Fluid Dynamics with Special Reference to Europe

Abstract

Fluid dynamics is study of motion of liquid and gases. One of the fundamental equation in fluid dynamics is the Navier-Stokes equation. It is equation of motion of fluid or gases in IR${}^{3}$. There is considerable work done on Navier-Stokes equation and Euler equation in decade. Existence and smoothness of solution for the Navier-Stokes equation in IR${}^{2}$ have been obtained. Leraythe French mathematician has shown that the Navier stokes equations is three dimensions have a weak solution. Ladyzhenskya studied the behavior of weak solutions of the Euler and Navier-Stokes equation. Solutions of the Navier-Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. In present paper researcher is comparing all the existing solution of Navier-Stokes equations and also reviewing finding obtained by European mathematicians on Solution of Navier-Stokes equations.