Dr. Sebastian Schwarzacher

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

Email: schwarz@karlin.mff.cuni.cz

Tel:   +420 221 913 414

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)



Primus Research Grant

The Primus Research Grant "The interactions of fluids and solids--On a systematic analysis theory for partial differential equations on variable domains in the context of fluid structure interactions" granted by the Charles University will initiate in January 2019. The project is granted for three years with a possible extension of two more years.

For this project we offer two postdoc positions. Please see here the announcement. Moreover, 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.

Winterterm 2018/2019:


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 JMAA 10.1016/j.jmaa.2018.10.055. 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.
  • L. Diening, P. Kaplicky, S. Schwarzacher: Campanato estimates for the generalized Stokes System. Ann. Mat. Pura Appl., (2014), vol. 193, p. 1779-1794 Preprint.
  • L. Diening, S. Schwarzacher: Global gradient estimates for the p(.)-Laplacian, Nonlinear Anal., (2014), vol. 106, p. 70-85 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

  • 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.