On the behavior in time of solutions to motion of Non-Newtonian fluids

Gioconda Moscariello, Maria Michaela Porzio
2020 NoDEA. Nonlinear differential equations and applications (Printed ed.)  
We study the behavior on time of weak solutions to the nonstationary motion of an incompressible fluid with shear rate dependent viscosity in bounded domains when the initial velocity u0∈L 2 . Our estimates show the different behavior of the solution as the growth condition of the stress tensor varies. In the "dilatant" or "shear thickening" case we prove that the decay rate does not depend on u0, then our estimates also apply for irregular initial velocity. Mathematics Subject Classification.
more » ... ct Classification. 76D03, 35Q35, 76D07 .
doi:10.1007/s00030-020-00645-9 fatcat:t2eqlklwmncypnwueskaetax5a