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.

Project description

Fluid solid interaction happens in many everyday instances. For example in the trachea where the air-flow inside the windpipe interacts with the cartilage surrounding it. The project aims to systematically develop an analysis for the related theory of partial differential equations. The scientific challenge is sub-summarized in the free interface between the solid and the fluid--the variable domain. Our objective is to advance the available mathematical theory in fluid-structure interaction towards the realistic case where both fluid and solid part are three-dimensional objects.

Members of the team:

We have regular group meetings every Thursday at 11 am in the common room of the Department of Mathematical Analysis where results are discussed and presented. Everybody is welcome.




Teaching

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

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.



Selected Publications

  • M. Bulicek, J. Burczak, S. Schwarzacher: Well posedness of nonlinear parabolic systems beyond duality, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, (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.



  • Recent Preprints

  • D. Breit, A. Cianchi, L. Diening, S. Schwarzacher: Global Schauder estimates for the p-Laplace system, (2019). Preprint.
  • 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, S. Byun, P. Kaplicky, J. Oh, S. Schwarzacher: On global Lq estimates for systems with p-growth in rough domains, (2018), Preprint.
  • V. Macha and S. Schwarzacher: Global BMO estimates for non-Newtonian fluids with perfect slip boundary conditions, (2017), Preprint.