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Dr. Thomas Eiter

Thomas Eiter
Address:
Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstraße 39
10117 Berlin, Germany
Phone: +49(0) 30 20372 398
Fax: +49(0) 30 20372 311
Email: thomas.eiter(at)wias-berlin.de
ORCID: ORCID logo 0000-0002-7807-1349  

I am a Young Investigator in the Collaborative Research Centre CRC 1114: Scaling Cascades in Complex Systems at Freie Universität Berlin.
Moreover, I am a member of the research group Partial Differential Equations at the Weierstrass Institute of Applied Analysis and Stochastics.

Scientific interests

My research focuses on the mathematical analysis of partial differential equations, usually motivated by problems from applied mathematics, in particular, fluid mechanics.
One of my major research topics concerns the motion of fluids in unbounded domains, for example, the flow past an obstacle. For the analytical investigation of such problems, already the choice of suitable function spaces can be a delicate aspect since it reflects the behavior of solutions at spatial infinity. I am also interested in the more detailed examination of the far-field behavior of the fluid flow, which I study in terms of fundamental solutions and the theory of singular integrals.
Moreover, I investigate classes of nonlinear PDEs where standard concepts like strong and weak solutions reach their limits, and a proper analysis requires the introduction of more generalized notions of solutions. This includes classical PDEs like hyperbolic conservation laws as well as complex models motivated from applications that include nonsmooth effects. In particular, I study solution concepts inspired by energetic considerations, using methods from nonlinear functional analysis and calculus of variations. This is also a topic of the project Analysis of energy-variational solutions for hyperbolic conservation laws associated to the SPP 2410.


Teaching [show/hide]
  • lecture course "Introduction to mathematical modeling with partial differential equations" at Freie Universität Berlin, winter term 2024/25 (whiteboard course)
  • lecture course "Harmonic analysis" at University of Kassel, summer term 2024 (moodle course)
  • student seminar "Analysis" at University of Kassel, summer term 2024 (moodle course)
  • lecture course "Funcional analysis" at University of Kassel, winter term 2023/24 (moodle course)
  • student seminar "Fachwissenschaftliches Seminar Mathematik, Lehramt Grundschule" at University of Kassel, winter term 2023/24 (moodle course)
  • student seminar "Fachwissenschaftliches Seminar Mathematik, Lehramt Haupt- und Realschule" at University of Kassel, winter term 2023/24 (moodle course)
  • lecture course "Multidimensional calculus of variations" at Humboldt-Universität zu Berlin, winter term 2022/23 (moodle course)
  • lecture course "Treffpunkt Mathematik III für Maschinenbau" at Technical University of Darmstadt, winter term 2019/20

Publications [show/hide]

Recent preprints

  1. T. Eiter, L. Schmeller.
    Weak solutions to a model for phase separation coupled with finite-strain viscoelasticity subject to external distortion.
    Preprint.  arXiv:2409.07066  WIAS Preprint No. 3130.
  2. T. Eiter, A.L. Silvestre.
    Representation formulas and far-field behavior of time-periodic flow past a body.
    Preprint.  arXiv:2402.12213  WIAS Preprint No. 3091.

Peer-reviewed articles

  1. T. Eiter, Y. Shibata.
    Viscous flow past a translating body with oscillating boundary.
    J. Math. Soc. Japan Advance Publication 2024. [Link]  arXiv:2303.09592  WIAS Preprint No. 3000.
  2. T. Eiter, R. Lasarzik.
    Existence of energy-variational solutions to hyperbolic conservation laws.
    Calc. Var. 63, 2024. [Link]  arXiv:2211.12307  WIAS Preprint No. 2974.
  3. T. Eiter, M. Kyed, Y. Shibata.
    Periodic Lp estimates by R-boundedness: Applications to the Navier–Stokes equations.
    Acta Appl. Math. 188, 2023. [Link]  arXiv:2204.11290  WIAS Preprint No. 2931.
  4. T. Eiter, M. Kyed, Y. Shibata.
    Falling drop in an unbounded liquid reservoir: Steady-state solutions.
    J. Math. Fluid Mech. 25, 2023. [Link]  arXiv:1912.04925.
  5. T. Eiter.
    On the regularity of weak solutions to time-periodic Navier–Stokes equations in exterior domains.
    Mathematics 11 (1), 2023. [Link]  arXiv:2212.00429  WIAS Preprint No. 2979.
  6. T. Eiter, K. Hopf, R. Lasarzik.
    Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models.
    Adv. Nonlinear Anal. 12 (1), 2023. [Link]  arXiv:2112.07480  WIAS Preprint No. 2904.
  7. T. Eiter.
    On the Oseen-type resolvent problem associated with time-periodic flow past a rotating body.
    SIAM J. Math. Anal. 54 (4), 2022. [Link]  arXiv:2111.00984  WIAS Preprint No. 2888.
  8. T. Eiter.
    On the Stokes-type resolvent problem associated with time-periodic flow around a rotating obstacle.
    J. Math. Fluid Mech. 24, 2022. [Link]  arXiv:2109.07949  WIAS Preprint No. 2876.
  9. T. Eiter, K. Hopf, A. Mielke.
    Leray–Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation.
    Nonlinear Anal. Real World Appl. 65, 2022. [Link]  arXiv:2104.05545  WIAS Preprint No. 2829.
  10. T. Eiter, G. P. Galdi.
    Spatial decay of the vorticity field of time-periodic viscous flow past a body.
    Arch. Rational Mech. Anal. 242, 2021. [Link]  arXiv:2011.12579  WIAS Preprint No. 2791.
  11. T. Eiter.
    On the spatially asymptotic structure of time-periodic solutions to the Navier–Stokes equations.
    Proc. Amer. Math. Soc. 159, 2021. [Link]  arXiv:2005.13268  WIAS Preprint No. 2727.
  12. T. Eiter, M. Kyed.
    Viscous flow around a rigid body performing a time-periodic motion.
    J. Math. Fluid Mech. 23, 2021. [Link]  arXiv:1912.04938.
  13. T. Eiter, M. Kyed, Y. Shibata.
    On periodic solutions for one-phase and two-phase problems of the Navier–Stokes equations.
    J. Evol. Equ. 21, 2021. [Link]  arXiv:1909.13558.
  14. T. Eiter, M. Kyed.
    Estimates of time-periodic fundamental solutions to the linearized Navier–Stokes equations.
    J. Math. Fluid Mech. 20, 2018. [Link] arXiv:1610.09249.

Book contributions

  1. T. Eiter, M. Kyed.
    Time-periodic linearized Navier–Stokes equations: An approach based on Fourier multipliers.
    In: T. Bodnár, G. P. Galdi, Š. Nečasová (eds.). Particles in flows, Adv. Math. Fluid Mech., 2017. [Link]

Conference proceedings

  1. T. Eiter, G. P. Galdi.
    New results for the Oseen problem with applications to the Navier–Stokes equations in exterior domains.
    In: RIMS Kôokyûuroku 2171, 2020. [Link] arXiv:1904.01527.

Dissertation thesis

  • T. Eiter.
    Existence and spatial decay of periodic Navier–Stokes flows in exterior domains.
    PhD thesis. 2020. (Logos Verlag Berlin, TUprints)

Other activities [show/hide]

Short CV [show/hide]
Since Oct 2024 Young Investigator in the Collaborative Research Centre CRC 1114: Scaling Cascades in Complex Systems at Freie Universität Berlin
Oct 2023 – Sep 2024 Interim professor ('Vertretungsprofessor') at the Institute of Mathematics of the University of Kassel
Since Apr 2020 Member of the research group Partial Differential Equations at the Weierstrass Institute of Applied Analysis and Stochastics
Feb 2020 Doctoral defense at Technical University of Darmstadt
Advisors: Prof. Mads Kyed (Flensburg), Prof. Reinhard Farwig (Darmstadt), Prof. Giovanni P. Galdi (Pittsburgh)
Oct 2016 – Mar 2020 Member of the Analysis Group at the Department of Mathematics of the Technical University of Darmstadt, and assistant in the project KI²VA
Oct 2014 – Sep 2016 Studies M.Sc. Mathematics at Technical University of Darmstadt
Oct 2011 – Sep 2014 Studies B.Sc. Mathematics at Technical University of Darmstadt

Thomas Eiter

Giving the Junior Richard-von-Mises-Lecture
(June 17, 2022)


Last modified: 2024-10-01 by Thomas Eiter
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