Nonlinear enhanced dissipation in viscous Burgers type equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914698683744256 |
|---|---|
| author | Ghoul, Tej-Eddine Masmoudi, Nader Pacherie, Eliot |
| author_facet | Ghoul, Tej-Eddine Masmoudi, Nader Pacherie, Eliot |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16839 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonlinear enhanced dissipation in viscous Burgers type equations Ghoul, Tej-Eddine Masmoudi, Nader Pacherie, Eliot Analysis of PDEs 34E13, 35B35, 35B40, 35B41 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. |
| title | Nonlinear enhanced dissipation in viscous Burgers type equations |
| topic | Analysis of PDEs 34E13, 35B35, 35B40, 35B41 |
| url | https://arxiv.org/abs/2211.16839 |