Concerning the Navier-Stokes problem

The problem discussed is the Navier-Stokes problem (NSP) in R 3 . Uniqueness of its solution is proved in a suitable space X . No smallness assumptions are used in the proof. Existence of the solution in X is proved for t ∈ [ 0 , T ] , where T > 0 is sufficiently small. Existence of the solution in X is proved for t ∈ [ 0 , ∞ ) if some a priori estimate of the solution holds.