Concentration-diffusion Effects in Viscous Incompressible Flows

Given a finite sequence of times 0 < t(1) <... < t(N), we construct an example of a smooth solution of the free nonstationnary Navier-Stokes equations in R(d), d = 2,3, such that: (1) The velocity field u(x,t) is spatially poorly localized at the beginning of the evolution but tends to concentrate until, as the time t approaches t(1), it becomes well-localized. (ii) Then u spreads out again after t(1), and such concentration-diffusion phenomena are later reproduced near the instants t(2), t(3), - - - -