IUMJ

Title: Concentration-diffusion effects in viscous incompressible flows

Authors: Lorenzo Brandolese

Issue: Volume 58 (2009), Issue 2, 789-806

Abstract:

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 .