2003/04/10 by Olivier Vallée, Olivier Vallee, Vallee, Olivier
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0304014
arxiv created 2003/04/10 · arxiv updated 2009/11/30
In this paper, we apply sensitivity methods to nonlinear PDEs like Burgers and KPZ equations. These equations are known to have analytical solutions which make easier the analysis of the sensitivity of their solutions to initial conditions. The main result stands in the fact that the most the solution is sensitive to the initial condition, the most it is decorrelated in space, i.e. the values of the initial condition participate to the solution at all distances of the wave front. This finally reveals a particular aspect of the Burgers turbulence.