On Application of Green Function Method to the Solution of 3D Incompressible Navier-Stokes equations

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton’s second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term- hence describing viscous flow. Due to specific of NS equations they could be transformed into full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Velocity and outer forces densities components were expressed in form of curl for obtaining solutions satisfying continuity condition specifying divergence of velocities equality to zero. Finally, solution in 3D space for any shaped boundary was expressed in terms of 3D Green function and inverse Laplace transform accordantly