We study the existence of weak solution for unsteady fluid-structure interaction problem for shear-thickening flow. The time dependent domain has at one part a flexible elastic wall. The evolution of fluid domain is governed by the generalized string equation with action of the fluid forces. The power-law viscosity model is applied to describe shear-dependent non-Newtonian fluids.
Anna HUNDERTMARK-ZAUŠKOVÁ. Mária LUKÁČOVÁ-MEDVIĎOVÁ. Šárka NEČASOVÁ. "On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid." J. Math. Soc. Japan 68 (1) 193 - 243, January, 2016. https://doi.org/10.2969/jmsj/06810193