Journal of the Mathematical Society of Japan

On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid

Anna HUNDERTMARK-ZAUŠKOVÁ, Mária LUKÁČOVÁ-MEDVIĎOVÁ, and Šárka NEČASOVÁ

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 1 (2016), 193-243.

Dates
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1453731541

Digital Object Identifier
doi:10.2969/jmsj/06810193

Mathematical Reviews number (MathSciNet)
MR3454559

Zentralblatt MATH identifier
1334.76032

Subjects
Primary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Secondary: 35D30: Weak solutions 76A05: Non-Newtonian fluids 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]

Keywords
non-Newtonian fluids fluid-structure interaction shear-thinning fluids shear-thickening fluids hemodynamics existence of weak solution

Citation

HUNDERTMARK-ZAUŠKOVÁ, Anna; LUKÁČOVÁ-MEDVIĎOVÁ, Mária; NEČASOVÁ, Šárka. On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid. J. Math. Soc. Japan 68 (2016), no. 1, 193--243. doi:10.2969/jmsj/06810193. https://projecteuclid.org/euclid.jmsj/1453731541


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