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

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.