## Differential and Integral Equations

### Asymptotic profiles for the third-grade fluids equations in one space dimension

M.A. Hamza

#### Abstract

In this article we consider the third-grade fluids equation in one space dimension. We show that the large time behavior of solutions is given by the very singular self-similar solutions of the associated Burgers equation. The proof of our result relies on the use of fine energy estimates in weighted spaces rewritten in the variables $\xi/\sqrt{\tau}$ and $\ln \tau$.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 1/2 (2015), 155-200.

Dates
First available in Project Euclid: 11 December 2014