Glasnik Matematicki, Vol. 56, No. 2 (2021), 407-440. \( \)

REGULARITY OF A WEAK SOLUTION TO A LINEAR FLUID-COMPOSITE STRUCTURE INTERACTION PROBLEM

Marija Galić

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10 000 Zagreb, Croatia
e-mail:marija.galic@math.hr

Abstract.   In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.

2020 Mathematics Subject Classification.   74F10, 76D03, 35M30

Key words and phrases.   Fluid-structure interaction, parabolic-hyperbolic coupling, regularity theory

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https://doi.org/10.3336/gm.56.2.11

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