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




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Research interests/Scientific background

Since February 2022 I am Associate Professor at the University of Uppsala. Simultaneously, 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. Further 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

Results have been achieved on compressible heat-conducting fluids (Breit, Sch, 2021, accepted at Annali della Scuola Normale di Pisa - Classe di Scienze ) the contactless rebound of elastic solids (Gravina, Sch, Soucek, Tuma, 2022, accepted in Journal of Fluid Mechanics) and the existence theory for bulk elastic solids with large deformations interacting with Navier-Stokes fluids. See (Benesova, Kampschulte, Sch, 2020, Preprint V) for the incompressible case and (Breit, Kampschulte, Sch, 2021, Preprint II), for the compressible case. Further we introduced the weak-strong uniqueness (Sch, Sroczinski, 2020, accepted at SIMA) of elastic plates interacting with incompressible fluids and a stable numeric approximation scheme for compressible fluids-structure interactions (Sch, She, 2022, accepted at Numerische Mathematik). Recently a general approach to invert the divergence equation in non-cylindrical domains was developed (Saari, Sch, 2021, Preprint III) and the existence of periodic solutions for fluid-structure interactions involving elastic plates (Mindrila, Sch, 2021, Preprint I).




Preprints

  1. D. Campbell, S. Hencl, A. Menovschikov, S. Schwarzacher: Injectivity in second-gradient Nonlinear Elasticity, (2021), Preprint.
  2. D. Breit, M. Kampschulte, S. Schwarzacher: Compressible fluids interacting with 3D visco-elastic bulk solids, (2021), Preprint.
  3. O.Saari, S. Schwarzacher: Construction of a right inverse for the divergence in non-cylindrical time dependent domains, (2021), Preprint.
  4. B. Benesova, M. Kampschulte, S. Schwarzacher: Variational methods for fluid-structure interaction and porous media (2021), Preprint.
  5. B. Benesova, M. Kampschulte, S. Schwarzacher: A variational approach to hyperbolic evolutions and fluid-structure interactions, (2020), Preprint.



Selected Publications

Find here a complete list of publications.

  • C. Mindrila, S. Schwarzacher: Time-periodic weak solutions for an incompressible Newtonian fluid interacting with an elastic plate, accepted on SIAM Journal on Mathematical Analysis, (2022), Preprint.
  • G. Gravina, S. Schwarzacher, O. Soucek, K. Tuma: Contactless rebound of elastic bodies in a viscous incompressible fluid, accepted in Journal of Fluid Mechanics, (2022), Preprint.
  • S. Schwarzacher, M. Sroczinski: Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation, accepted on SIAM Journal on Mathematical Analysis, (2022), Preprint.
  • S. Schwarzacher, B. She: On numerical approximations to fluid-structure interactions involving compressible fluids, (2022), accepted in Numerische Mathematik 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, Preprint.
  • D. Breit, A. Cianchi, L. Diening, S. Schwarzacher: Global Schauder estimates for the p-Laplace system, accepted in Arch. Rat. Mech. Anal, (2021) Preprint.
  • B. Muha, S. Schwarzacher: Existence and regularity for weak solutions for a fluid interacting with a non-linear shell in 3D, accepted in Annal. l'Inst. H. Poinc. (C) Anal. Non Lin., (2021), Preprint.
  • 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

    Winterterm 2020/2021:

    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.