Differential and Integral Equations

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

M.A. Hamza

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1418310425

Mathematical Reviews number (MathSciNet)
MR3299121

Zentralblatt MATH identifier
1349.76010

Subjects
Primary: 76A05: Non-Newtonian fluids 35C06: Self-similar solutions 35B40: Asymptotic behavior of solutions

Citation

Hamza, M.A. Asymptotic profiles for the third-grade fluids equations in one space dimension. Differential Integral Equations 28 (2015), no. 1/2, 155--200. https://projecteuclid.org/euclid.die/1418310425


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