Solution of the Navier-Stokes problem

A new a priori estimate for solutions to Navier-Stokes equations is derived. Uniqueness and existence of these solutions in R3 for all t>0 is proved in a class of solutions locally differentiable in time with values in H1(R3), where H1(R3) is the Sobolev space. By the solution a solution to an integral equation is understood. No smallness restrictions on the data are imposed.