A fundamental problem in mathematics is to decide whether such smooth, physically reasonable solutions exist for the Navier-Stokes equations. We restrict attention here to incompressible fluids filling all of  The Cauchy problem for the nD Navier-Stokes equations is reduced to the integral equations of Volterra and Volterra-Abel, investigation of which, allows us to solve positively question on uniqueness and smoothness of the solution.

Navier-Stokes equation, partial differential equation (PDE), incompressible fluid, small viscosity.