Sebastian Schwarzacher

Short presentation

Research interests:

• Nonlinear partial differential equations
• Fluid dynamics, fluid-structure interactions
• Calculus of variations
• Theory of Numerics for PDEs
• Analysis of evolutionary non-linear PDEs

Further, I am the head of the Centre of analysis and numerics for fluid-structure interactions at Charles University. The research focus on the mathematics for the interactions between (elastic) solids and (viscous) fluids.

Keywords

• fluid dynamics
• analysis
• solid-liquid interfaces
• partial differential equations
• solid-fluid and heat interactions

Biography

List of publications

Orcid

Google Scholar

MathSciNet

Preprints

• I. D. Breit S. Schwarzacher, The Stokes problem with Navier boundary conditions in irregular domains, (2025). Preprint.
• II. S. Mosny, B. Muha, S. Schwarzacher, J. Webster, Time-Periodic Solutions for Hyperbolic-Parabolic Systems, (2024). Preprint.
• III. M. Kampschulte, J. Niinikoski, S. Schwarzacher, Regularity estimates of a fluid-free surface evolution, (2024). Preprint.
• IV. S. Almi, R. Badal, M. Friedrich, S. Schwarzacher, Thermo-elastodynamics of nonlinearly viscous solids, (2024). Preprint.
• V. D. Breit, P. R. Mensah, S. Schwarzacher, P. Su: Ladyzhenskaya-Prodi-Serrin condition for fluid-structure interaction systems, (2023). Preprint.
• VI. C. Mindrila, S. Schwarzacher: Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions, (2023). Preprint.

Research

Recent progress

• Time periodic solutions for parabolic PDEs interacting with hyperbolic PDEs. Newly developed quantitative a-priori estimates depending on the geometry of the wave-domain are introduced. These lead to general well-posedness results for domains satisfying geometrical assumptions. (Mosny, Muha, Sch, Webster Preprint II).
• Higher order energy estimates for fluid with a free surface are shown. These are geometrically intrinsic regularity estimates. (Kamschulte, Niinikoski, Sch Preprint III).
• Existence of smooth solutions for a beam interacting with the 2D Navier-Stokes equations (Sch, Su, 2025, CMP).
• Conditional regularity and uniqueness for fluid-structure interactions involving 3D Navier Stokes (Breit, Mensah, Sch, Su, Preprint V).
• Convergence results for finite element approximations involving time-changing geometry (Sch, She, Tuma, Num. Math.).
• Existence of time-periodic solutions for fluid-structure interactions involving elastic shells (Mindrila, Sch, Preprint VI) and plates (Mindrila, Sch, 2022, SIMA).
• Existence theory for bulk elastic solids with large deformations interacting with Navier-Stokes fluids. See (Benesova, Kampschulte, Sch, JEMS) for the incompressible case and (Breit, Kampschulte, Sch, Math. Annal.), for the compressible case. For numerical approximation schemes along the method, see (Cesik, Sch, JDE) and for thermo-elastodynamics see (Almi, Badal, Friedrich, Sch, Preprint IV).
• A general approach to invert the divergence equation in non-cylindrical domains, (Saari, Sch, Annals of PDE).
• Contactless rebound of elastic solids (Gravina, Sch, Soucek, Tuma, 2022, JFM) and (Fara, Sch, Tuma, CMAME)