The Centre of analysis for the interaction of fluids and solids was initiated at the beginning of 2019 and since Fall 2022 is mainly financed through the ERC-CZ Grant LL2105 CONTACT.
Currently the team has 13 members.
The research is focused on the interactions between fluids and solids. Fluid solid interaction happens in many everyday instances. For example blood flow through a vessel or air flow through the trachea, oscillations of suspension bridges, lifting of airplanes, bouncing of elastic balls, or the rotation of wind turbines. The working group aims to systematically develop an analysis for the related theory of partial differential equations. We attack classical questions of existence, uniqueness, regularity and stability, questions about the qualitative behavior of fluids interacting with solids and the quantification of the forces at the free interface between the solid and the fluid-the variable domain. Moreover, we progress in the field of scientific computing and modeling. In case you wish to participate in the program please contact me for more information.

Current main scientific activities

Here you find news and preprints.

• Elastic plates interacting with fluids. Smooth solutions for a beam interacting with the 2D Navier-Stokes equations were constructed, see (Schwarzacher, Su, 2023). Weak-strong uniqueness for elastic shells interacting with the 3D Navier-Stokes equation was shown see (Breit, Mensah, Schwarzacher, Su, 2023). Weak solutions involving displacements in all coordinate directions are studied for which existence could be shown (Kampschulte, Sch, Sperone, 2023, JMPA).
• A variational approach to fluid-structure interactions. Existence of weak solutions for 3D solids interacting with 3D fluids via DeGiorgi's celebrated minimizing movements method (Benesova, Kampschulte, Sch, 2024, JEMS). The method could recently be advanced to compressible fluids, see (Breit, Kampschulte, Schwarzacher, 2024, Math. Anal.) For a survey article that introduces the variational methodology at the example of porous media please see (Benesova, Kampschulte, Schwarzacher, Nonlin. Anal. RWA). Current projects are to extend the method to more solids and contact problems. For solids progress was achieved in (A. Cesik, G. Gravina, M. Kampschulte, 2024, Calc. Var. PDE). Further numerical approximation schemes along the method have been initiated (Cesik, Schwarzacher, 2025, JDE).
• Numerical approximation of fluid-structure interaction. Convergence results and experiments for finite element approximations can be found in (Schwarzacher, She, Tuma, 2025, Num. Math.). The development of (stable) schemes here (Schwarzacher She, 2022, Num. Math.). A long term aim is the study on adaptive methods to obtain fast solvers for ALE based solvers. See Numerics for more information.
• Bouncing of elastic objects in a fluid. We investigate the possibility of bouncing for solid objects hitting a wall in a viscous fluid. It is known that for no-slip boundary condition no contact of the solid with the wall is happening. We aim to find the necessary and sufficient elastic properties of the solid in order to bounce of the ground, even so no contact is happening. First theoretical and numerical investigations can be found here (Gravina, Sch, Soucek, Tuma, 2023, JFM). For further numerical strategies and results see (Fara, Schwarzacher, Tuma 2023).
• Time-periodic solutions The appearance of time-periodic motions in fluid-structure interactions is investigated. Numerically by studies on the traction forces (with Cach, Fehling and Tuma). Analytically by providing existence results. Here the estimate of the diffusive impact of the fluid on the (hyperbolic) solid is crucial. In (Mosny, Muha, Schwarzacher, Webster, 2024) the uniqueness and existence for a heat-wave coupling was shown. There it was shown that depending on the geometry of the wave domain the diffusive impact of the heat can be strong enough for a-priori estimates. However, with significant loss in regularity. A different line of research is on elastic shells interacting with Navier Stokes equations, where a theory for linear solids was developed (Mindrila, Schwarzacher 2022, 2023).
• Further subjects. Free boundary problems in fluid-mechanics. Higher order energy estimates were developed here ( Kampschulte, Niinikoski, Schwarzacher, 2024). Plasticity and fluid-structure interactions (Benesova, Biswas, Kampschulte, Schwarzacher). Temperature effects. See (Breit, Schwarzacher, Ann. Sc. Norm. Sup. Pisa 2023, 24(2), pp. 619–690) and (Almi, Badal, Friedrich, Schwarzacher 2024).

Funding

The Ministry of Education, Youth and Sport of the Czech Republic (MSMT) supports the centre via the Grant LL2105 CONTACT from 09/2021 until 08/2026. Further we thank the support of the University Centre MathMAC (UNCE/SCI/023) and (UNCE/24/SCI/005), and the Swedish research council via the VR Grant 2022-03862.