Nonlinear enhanced dissipation in viscous Burgers type equations II

Abstract

In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of infinite mass initial datas. We show that an enhanced dissipation effect occurs generically, that is the decay rate in time is better than if we considered instead the heat equations for the same inital value. We also show the existence of a kind of global attractor per class.

KEYWORDS:

• asymptotic profiles
• nonlinear analysis
• self similar transformations

Disclosure statement

The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Funding

The authors are supported by Tamkeen under the NYU Abu Dhabi Research Institute grant CG002.