Sebastian Schwarzacher

Department of Mathematical Analysis
Faculty of Mathematics and Physics
Charles University
Sokolovská 83
186 75 Praha 8

Email: schwarz@karlin.mff.cuni.cz

Tel: (+420) 2 2191 3267

Curriculum Vitae

List of publications

Orcid (external)

Google Scholar (external)

MathSciNet (external)

Since February 2022 I am Associate Professor at the University of Uppsala

Research interests/Scientific background

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. It is for large parts supported by the ERC-CZ Grant LL2105 CONTACT. Since February 2022 I am also Associate Professor at the University of Uppsala. Fields of my research activity are:

Nonlinear partial differential equations (existence, uniqueness, regularity, numerical analysis)
Fluid dynamics (Fluid-structure interactions, compressible fluids, non-Newtonian Fluids)
Calculus of variations (non-standard growth, rate independent systems, elastic solids)
Theory of Numerics for PDEs (time schemes, convergence rates, Galerkin methods)
Analysis of evolutionary non-linear PDEs (variable domains, intrinsic geometry, systems with variable contact interface)

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, Preprint V).
Conditional regularity and uniqueness for fluid-structure interactions involving 3D Navier Stokes (Breit, Mensah, Sch, Su, Preprint VI).
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 VII) 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)

Preprints

D. Breit S. Schwarzacher, The Stokes problem with Navier boundary conditions in irregular domains, (2025). Preprint.

S. Mosny, B. Muha, S. Schwarzacher, J. Webster, Time-Periodic Solutions for Hyperbolic-Parabolic Systems, (2024). Preprint.

M. Kampschulte, J. Niinikoski, S. Schwarzacher, Regularity estimates of a fluid-free surface evolution, (2024). Preprint.

S. Almi, R. Badal, M. Friedrich, S. Schwarzacher, Thermo-elastodynamics of nonlinearly viscous solids, (2024). Preprint.

S. Schwarzacher, P. Su: Regularity for an elastic beam interacting with 2D Navier-Stokes equations, (2023). Preprint.

D. Breit, P. R. Mensah, S. Schwarzacher, P. Su: Ladyzhenskaya-Prodi-Serrin condition for fluid-structure interaction systems, (2023). Preprint.

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.

D. Campbell, S. Hencl, A. Menovschikov, S. Schwarzacher: Injectivity in second-gradient Nonlinear Elasticity, (2021), Preprint.

Selected Publications

Find here a complete list of publications.

S. Schwarzacher, B. She, K. Tuma: Stability and error estimates of a linear numerical scheme approximating nonlinear fluid-structure interactions, (2025), accepted at Numerische Mathematik, Preprint.

A. Cesik, S. Schwarzacher: Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization, J.~Diff.~Eq., Vol. 415, (2025), 434-486, Paper.

D. Breit, M. Kampschulte, S. Schwarzacher: Compressible fluids interacting with 3D visco-elastic bulk solids, Math. Annal., (2024), 1-58, Paper.

J. Fara, S. Schwarzacher, K. Tuma: Geometric re-meshing strategies to simulate contactless rebounds of elastic solids in fluids, Computer Methods in Applied Mechanics and Engineering, Vol. 422, (2024), Paper.

B. Benesova, M. Kampschulte, S. Schwarzacher: A variational approach to hyperbolic evolutions and fluid-structure interactions, JEMS, (2023), DOI 10.4171/JEMS/1353, Paper.

M. Kampschulte, S. Schwarzacher, G. Sperone: Unrestricted deformations of thin elastic structures interacting with fluids (2023), JMPA, Vol. 173, p. 96-148 Paper.

O.Saari, S. Schwarzacher: Construction of a right inverse for the divergence in non-cylindrical time dependent domains, (2023), Annals of PDE, Vol. 9, p. 8 Paper.

C. Mindrila, S. Schwarzacher: Time-periodic weak solutions for an incompressible Newtonian fluid interacting with an elastic plate, SIMA, Vol. 54, p. 4139-4162, (2022), Paper.

B. Benesova, M. Kampschulte, S. Schwarzacher: Variational methods for fluid-structure interaction and porous media (2021), Nonlinear Analysis RWA, Vol. 71, p. 103819 Paper.

G. Gravina, S. Schwarzacher, O. Soucek, K. Tuma: Contactless rebound of elastic bodies in a viscous incompressible fluid, Journal of Fluid Mechanics, Vol. 942, p. A34, (2022), Paper.

S. Schwarzacher, M. Sroczinski: Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation, SIAM Journal on Mathematical Analysis, Vol. 54, p. 4104-4138, (2022), Paper.

S. Schwarzacher, B. She: On numerical approximations to fluid-structure interactions involving compressible fluids, Numerische Mathematik, Vol. 151, p. 219-278,(2022), Preprint.

D. Breit and S. Schwarzacher: Navier-Stokes-Fourier fluids interacting with elastic shells, (2021), accepted at Annali della Scuola Normale di Pisa - Classe di Scienze, Vol. 24, p. 619?690, (2023), Preprint.

D. Breit, A. Cianchi, L. Diening, S. Schwarzacher: Global Schauder estimates for the p-Laplace system, Arch. Rat. Mech. Anal, Vol. 243, p. 201-255, (2022), Paper.

B. Muha, S. Schwarzacher: Existence and regularity for weak solutions for a fluid interacting with a non-linear shell in 3D, Annal. l'Inst. H. Poinc. (C) Anal. Non Lin., Vol. 6, p. 1369-1412, (2022), Paper.

R. Hofer, K. Kowalczyk, S. Schwarzacher: Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains, Vol. 31, p. 1787 - 1819, (2021). Preprint.

C. Mindrila, S. Schwarzacher: Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors, JDE, Vol. 279, p. 10-45, (2021). Preprint.

F. Rindler, S. Schwarzacher, J. J. L. Velazquez: Two-speed solutions to non-convex rate-independent systems, Arch. Rat. Mech. Anal., Vol. 239, p. 1667-1731 (2021). Preprint.

U. Gianazza and S. Schwarzacher: Self-improving property of the fast diffusion equation, JFA, Vol. 277, p. 108291, (2019). Preprint.

M. Bulicek, J. Burczak, S. Schwarzacher: Well posedness of nonlinear parabolic systems beyond duality, Annal. l'Inst. H. Poinc. (C) Anal. Non Lin., Vol. 36, p. 1467-1500, (2019). Preprint.

U. Gianazza and S. Schwarzacher: Self-improving property of degenerate parabolic equations of porous medium-type, (2019), Amer. J. Math., Vol. 141, p. 399-446. Preprint.

Y. Lu and S. Schwarzacher: Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes (2018), JDE 265 (4), 1371-1406. Preprint.

D. Breit and S. Schwarzacher: Compressible fluids interacting with a linear-elastic shell, Arch. Rat. Mech. Anal, (2018), Vol. 228, p. 495-562. Preprint.

D. Breit, A. Cianchi, L. Diening, T. Kuusi and S. Schwarzacher: Pointwise Calderon-Zygmund gradient estimates for the p-Laplace system, JMPA, (2018), Vol.114, p. 146-190. Preprint.

F. Rindler, S. Schwarzacher, E. Suli: Regularity and approximation of strong solutions to rate-independent systems, M3AS, (2017), Vol.27, p. 2511-2556. Preprint.

L. Diening, S. Schwarzacher, B. Stroffolini and A. Verde: Parabolic Lipschitz truncation and Caloric Approximation, Calc. of Var. and PDE, (2017), Vol. 56, p. 120. Preprint.

M. Bulicek, J. Burczak and S. Schwarzacher: A unified theory for some non Newtonian fluids under singular forcing, SIAM J. Math. Anal., (2016), vol. 48, p. 4241–4267. Preprint.

M. Bulicek and S. Schwarzacher: Existence of very weak solutions to elliptic systems of p-Laplacian type, Calc. of Var. and PDE, (2016), vol. 55, 14 pp Preprint.

M. Bulicek, L. Diening and S. Schwarzacher: Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems, Analysis and PDE, (2016), vol. 9, p. 1115–1151 Preprint.

J. Frehse, S. Schwarzacher: On regularity of the time derivative for degenerate parabolic systems, SIAM J. Math. Anal., (2015), vol. 47, p.3917-3943 Preprint.

D. Breit, L. Diening, S. Schwarzacher: Finite element methods for the p(.)-Laplacian, SIAM J. Numer. Anal., (2015), vol. 53, p. 551-572 Preprint.

S. Schwarzacher: Hölder-Zygmund Estimates for Parabolic Degenerate Systems. J. Differential Equations, (2014), vol. 256, p. 2423-2448 Preprint.

D. Breit, L. Diening, S. Schwarzacher: Solenoidal Lipschitz truncation for parabolic PDE's. Math. Models Methods Appl. Sci., (2013), vol. 23, p. 2671-2700 Preprint.

L. Diening, Ch. Kreuzer, S. Schwarzacher: Convex Hull Property and Maximum Principles for Finite Element Minimizers of General Convex Functionals. Numer. Math. (2013), vol. 124, p. 685-700. Preprint.

L. Diening, P. Kaplicky, S. Schwarzacher: BMO estimates for the p-Laplacian, Nonlinear Anal., (2012), Vol. 75, p. 637-650, Preprint.

Teaching in Prague (until 2021)

Winterterm 2020/2021:

Partial differential equations 1. Tuesday 17.20-18.05 K9 and Wednesday 11.30-13.00 K9. Find here a link to some lecture notes . Find here a link to the homework-sheets.

Summerterm 2021:

Mathematics 2 (for FSV UK). Tuesday at 14.00 and Wednesday at 12:30 online. Find here the slides of the lecture. Find here the link to the web page of the related tutorial classes. Find here a link to the moodle.

Winterterm 2020/2021:

Mathematics 1 (for FSV UK). Wednesday 11.00 and Thursday 9:30 online. Find here the slides of the lecture. Find here the link to the web page of the related exercise classes. Find here a link to the recorded lectures.
Lecture NMMA531, Partial differential equations 3. Monday 14.00 online. Literature (Part I): L.C. Evans, Partial Differential Equations, Graduate studies in mathematics, ISSN 1065-7339.

Summerterm 2020:

Partial differential equations 2. Monday 15.40-17.10 K4 and Wednesday 14.50-15.35 K7. Find here a link to some lecture notes . Find here a link to the homework-sheets. Link to E-Lecture for Partial differential equations 2.

Winterterm 2019/2020:

Partial differential equations 1. Wednesday 17.20-18.05 K9 and Thursday 11.30-13.00 K6. Find here a link to some lecture notes . Find here a link to the homework-sheets.

Summerterm 2019:

Mathematics 2 (for FSV UK). Tuesday 15:30 and Wednesday 11:00 in O 105. Find here the slides of the lecture.
The written final exam is Tuesday 28.6.2019 in lecture hall K2 in Sokolovská 83 (2nd floor) from 14.00-15.30.

Winterterm 2018/2019:

Mathematics 1 (for FSV UK). Wednesday 9:30 and Thursday 11:00 in O 105. Find here the slides of the lecture. Find here the link to the web page of the related exercise classes.
The written final exam is Monday 21.1.2019 in lecture hall O 105 from 9.30-11.00.
Mathematics 1 - Repetitorium (for FSV UK). Friday 9:30 in O 105.
Lecture K433KNM, Partial differential equations III. Monday at 14.00 in the seminar room of the KNM MFF UK (Karlin, 4th floor).

Summerterm 2017:

Mathematics 2 (for FSV UK). Tuesday 15:30 and Wednesday 12:30 in O 105.
Seminar on Differential Equations - NMMA431, Elliptic partial differential equations and free boundary problems. Anouncement.

Winterterm 2016/2017:

Analysis for instationary partial differential equations. Monday 10:40-12:20 in K9. Anouncement.