Differentiability of the solution operator and the dimension of the attractor for certain power-law fluids

Abstract

We study the dynamics of a two-dimensional homogenenous incompressible fluid of power-law type, with the viscosity behaving like $(1+|\Du|)^{p-2}$, $p\ge2$. Here $\Du$ is the symmetric velocity gradient.

Thanks to the recent regularity results of Kaplick\'y, M\'alek and Star\'a, we prove that the solution operator is differentiable. This enables us to use the Lyapunov exponents to estimate the dimension of the exponential attractor.

Keywords

• Differentiability
• solution
• operator
• dimension
• attractor
• certain
• power-law
• fluids