Euler equation for incompressible non-Newtonian fluids: finite speed of propagations and asymptotic behavior of weak solutions

TL;DR

This paper studies a multidimensional model for incompressible non-Newtonian fluids, proving finite speed of propagation of solutions and establishing sharp bounds based on initial data norms.

Contribution

It introduces a method to prove finite speed of propagation for non-Newtonian fluids and derives precise bounds using energy estimates.

Findings

Finite speed of propagation of solutions

Sharp bounds based on initial data norms

Energy estimates method applied to non-Newtonian fluids

Abstract

We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the propagations by $L^2$--norm and $L^1$--norm of initial data.