Dr. Sebastian Schwarzacher

Katedra matematické analýzy
Matematicko-fyzikální fakulta Univerzity Karlovy
Sokolovská 83
186 75 Praha 8

Email: schwarz@karlin.mff.cuni.cz

Tel:   (+420) 2 2191 3267

Curriculum Vitae

Orcid (external)

Google Scholar (external)

MathSciNet (external)


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Research interests

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



Project on the interaction of fluids and solids

Funding for the project is provided by a Junior Grant of the Czech Science Foundation and a Primus Research Programme of Charles University. The funding is for three years with a possible extension of two more years of the Primus grant.

For this project we have three postdoc positions and two PhD positions. Postdocs and students that are looking for a PhD position or a master theses related to the subject are invited to contact Barbora Benesova or myself.




Teaching

Students that are interested in a Bachelor, Master or PhD thesis can find here a list of subjects.

Summerterm 2019:

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.



Selected Publications

  • 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.
  • U. Gianazza and S. Schwarzacher: Self-improving property of degenerate parabolic equations of porous medium-type (2018), Accepted at AJM Preprint.
  • D. Breit and S. Schwarzacher: Compressible fluids interacting with a linear-elastic shell ARMA, (2018), Vol. 228, p. 495-562. 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, (2018), Vol. 56, p. 120. Preprint.
  • D. Breit, A. Cianchi, L. Diening, T. Kuusi and S. Schwarzacher: Pointwise Calderon-Zygmund gradient estimates for the p-Laplace system, JMPA, (2017), Vol.114, p. 146-190. 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.



  • Recent Preprints

  • E. Chiodaroli, O. Kreml, V. Macha, S. Schwarzacher: Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data, (2018). Preprint.
  • U. Gianazza and S. Schwarzacher: Self-improving property of the fast diffusion equation, (2018). Preprint.
  • M. Bulicek, J. Burczak, S. Schwarzacher: Well posedness of nonlinear parabolic systems beyond duality, (2018). Preprint.
  • M. Bulicek, S. Byun, P. Kaplicky, J. Oh, S. Schwarzacher: On global Lq estimates for systems with p-growth in rough domains, (2018).
  • V. Macha and S. Schwarzacher: Global BMO estimates for non-Newtonian fluids with perfect slip boundary conditions, (2017), Preprint.