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Interaction of Finitely-Strained Viscoelastic Multipolar Solids and Fluids by an Eulerian Approach

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A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin–Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The no-slip contact between fluid and solid is considered and the Eulerian-frame return-mapping technique is used for both the fluid and the solid models, which allows for a “monolithic” formulation of this fluid–structure interaction problem. Existence and a certain regularity of weak solutions is proved by a Schauder fixed-point argument combined with a suitable regularization.

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Inspiring discussions with Sebastian Schwarzacher during author’s stay at University of Vienna in 2020 are deeply acknowledged. Moreover, the author is also thankful to two anonymous referees for numerous comments and suggestions having lead to improvement of the presentation. Also the support from MŠMT ČR (Ministry of Education of the Czech Republic) project CZ.02.1.01/0.0/0.0/15-003/0000493, and from the institutional support RVO:61388998 (ČR) is acknowledged.

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Correspondence to Tomáš Roubíček.

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Roubíček, T. Interaction of Finitely-Strained Viscoelastic Multipolar Solids and Fluids by an Eulerian Approach. J. Math. Fluid Mech. 25, 81 (2023).

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