Concentration-diffusion effects in viscous incompressible flows Lorenzo Brandolese 76D0535Q30Navier-Stokesasymptotic profilesasymptotic behaviorfar-fieldflow mapanalyticitysymmetryspatial spreadinglower boundpointwise estimatesdecay ratesingularities Given a finite sequence of times $0 < t_{1} < \dots < t_{N}$, we construct an example of a smooth solution of the free nonstationnary Navier-Stokes equations in $\mathbb{R}^d$, $d = 2,3$, such that: (i) 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 $t_{2}$, $t_{3}$, \dots . Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3504 10.1512/iumj.2009.58.3504 en Indiana Univ. Math. J. 58 (2009) 789 - 806 state-of-the-art mathematics http://iumj.org/access/