ON THE CAUCHY PROBLEM OF NAVIER-STOKES FLOW

Consider the Cauchy semilinear problem of the Navier-Stokes flow of incompressible fluids - one of the Millenium Prize Problems (see [1]). By standard arguments we can formulate the problem as an abstract equation and prove the existence and the uniqueness of the strong solution. The proof is constructive and it is based on the Fourier method developed in the energetical space of the Stokes operator (on the complete sequence of the eigenvectors of the duality map). Some open problems are also appended.