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)




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Research interests/Scientific background

  • 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)
In the last years I specialized in the research on the mathematics for the interactions between (elastic) solids and (viscous) fluids. The research is supported by my working group. For more information on my working group please see the next paragraph.



Working group: Interaction of Fluids and Solids

The working group on the Interaction of Fluids and Solids was initiated at the beginning of 2019 and is mainly financed through third party funding. For details please see the end of the paragraph.

New! ERC-CZ Grant LL2105 INTERACT starting in September.

The Ministry of Education, Youth and Sport of the Czech Republic supports the Grant LL2105 INTERACT from 09/2021 until 08/2026. For this program please apply to the following open postdoc position.

Research description

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 interchange ideas with the field of scientific computing and modeling and progress the related theory of numerical approximation schemes.

Current main scientific activities

Recent results

Results have been achieved on compressible heat-conducting fluids (Breit, Sch, 2021, Preprint IV) the contactless rebound of elastic solids (Gravina, Sch, Soucek, Tuma, 2020, Preprint V) and the existence theory for bulk elastic solids with large deformations interacting with Navier-Stokes fluids. See (Benesova, Kampschulte, Sch, 2020, Preprint VI for the incompressible case and (Breit, Kampschulte, Sch, 2021, Preprint I), for the compressible case. Further we introduced the weak-strong uniqueness (Sch, Sroczinski, 2020, Preprint VII) of elastic plates interacting with incompressible fluids and a stable numeric approximation scheme for compressible fluids-structure interactions (Sch, She, 2020, Preprint VIII). Very recently a general approach to invert the divergence equation in non-cylindrical domains was developed (Saari, Sch, 2021, Preprint II).

Team members

Former team members

Postdoc: Giovanni Gravina (now Temple Univ.), Matthias Sroczinski (now Univ. of Konstanz), Jan Burczak (now Univ. of Leipzig).

Group meetings

During the semester we have regular online group meetings every Wednesday at 15.00 where results are discussed and presented. Everybody is welcome to join. In case of interest please send an email.

Funding

Funding for the project is provided by the support of the Junior Grant (GJ19-11707Y) of the Czech Science Foundation and by the Primus Research Programme (PRIMUS/19/SCI/01) of Charles University. Starting from September 2021 the group will be financed by the ERC-CZ Grant LL2105 INTERACT. Several members of the working group are additionally supported by the University Centre MathMAC (UNCE/SCI/023).

Poster (on the occasion of the Annual meeting of PRIMUS investigators 2020).


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Teaching

Summerterm 2021:

Winterterm 2020/2021:

Summerterm 2020:

Winterterm 2019/2020:

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.



Recent Preprints

  1. D. Breit, M. Kampschulte, S. Schwarzacher: Compressible fluids interacting with 3D visco-elastic bulk solids, (2021), Preprint.
  2. O.Saari, S. Schwarzacher: Construction of a right inverse for the divergence in non-cylindrical time dependent domains, (2021), Preprint.
  3. B. Benesova, M. Kampschulte, S. Schwarzacher: Variational methods for fluid-structure interaction and breathing through masks, (2021), Preprint.
  4. D. Breit and S. Schwarzacher: Navier-Stokes-Fourier fluids interacting with elastic shells, (2021), Preprint.
  5. G. Gravina, S. Schwarzacher, O. Soucek, K. Tuma: Contactless rebound of elastic bodies in a viscous incompressible fluid, (2020), Preprint.
  6. B. Benesova, M. Kampschulte, S. Schwarzacher: A variational approach to hyperbolic evolutions and fluid-structure interactions, (2020), Preprint.
  7. S. Schwarzacher, M. Sroczinski: Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation, (2020), Preprint.
  8. S. Schwarzacher, B. She: On numerical approximations to fluid-structure interactions involving compressible fluids, (2020), Preprint.
  9. O. Saari, S. Schwarzacher: A reverse Hölder inequality for the gradient of solutions to Trudinger's equation, (2019), Preprint.
  10. B. Muha, S. Schwarzacher: Existence and regularity for weak solutions for a fluid interacting with a non-linear shell in 3D, (2019), Preprint.
  11. D. Breit, A. Cianchi, L. Diening, S. Schwarzacher: Global Schauder estimates for the p-Laplace system, (2019), Preprint.



Selected Publications

Find here a complete list of publications.

  • R. Hofer, K. Kowalczyk, S. Schwarzacher: Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains, accepted at M3AS (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, ARMA, 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), American Journal of Mathematics, 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, ARMA, (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.