2022/11/30 by Tej‐Eddine Ghoul, Nader Masmoudi, Ghoul, Tej-Eddine +3
Engineering · Mathematics · Earth and Planetary Sciences · #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Meteorological Phenomena and Simulations
paper · pdf · doi:10.48550/arxiv.2211.16839
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation coming from a nonlinear transport term. We compute the asymptotic profile in this class for both equations. For the viscous Burgers equation, the main novelty is the construction and description of a time dependent profile with a boundary layer, which enhanced the dissipation. This profile will be stable up to a computable nonlinear correction depending on the perturbation. We also extend our results to other convection-diffusion equations.