Backward time behavior of dissipative PDE [electronic resource] /

by Dascaliuc, Radu

We study behavior for negative times t of the 2D periodic Navier-Stokes equations and Burgers' original model for turbulence. Both systems are proved to have rich sets of solutions that exist for all t [isin] R and increase exponentially as t [rarr] - [Infinity]. However, our study shows that the behavior of these solutions as well as the geometrical structure of the sets of their initial data are very different. As a consequence, Burgers original model for turbulence becomes the first known dissipative system that despite possessing a rich set of backward-time exponentially growing solutions, does not display any similarities, as t [rarr] -[Infinity], to the linear case.