Backward time behavior of dissipative PDE

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Title: Backward time behavior of dissipative PDE
Author: Dascaliuc, Radu
Abstract: 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 - R and increase exponentially as t - > - (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 - > - (Infinity ) , to the linear case .
URI: http : / /hdl .handle .net /1969 .1 /4940
Date: 2007-04-25

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Backward time behavior of dissipative PDE. Available electronically from http : / /hdl .handle .net /1969 .1 /4940 .

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