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In to previous papers by the authors, classes of initial data to the threedimensional, incompressible Navier-Stokes equations were presented, generatinga global smooth solution although the norm of the initial data may be chosenarbitrarily large. The aim of this article is to provide new examples ofarbitrarily large initial data giving rise to global solutions, in the wholespace. Contrary to the previous examples, the initial data has no particularoscillatory properties, but varies slowly in one direction. The proof uses thespecial structure of the nonlinear term of the equation.

Large, global solutions to the Navier-Stokes equations, slowly varying in one direction