Dr. 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: 0000-0002-7807-1349

Scientific interests My research focuses on mathematical fluid mechanics and the analysis of associated partial differential equations. One of my research topics concerns the motion of fluids in unbounded domains, for example, the flow past an obstacle. Here, one difficulty is to find a functional framework suitable for existence of stationary and time-periodic solutions to the corresponding Navier–Stokes equations. The corresponding function spaces also yield information on the behavior of the fluid flow in the far field, which is further studied 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. I am interested in solution concepts inspired by energetic considerations, and for their study I use methods from nonlinear functional analysis and calculus of variations. Current teaching activities In the winter term 2022/23, I gave the lecture course "Multidimensional calculus of variations" at Humboldt-Universität zu Berlin, together with Matthias Liero. For further information, please visit the moodle website (Link). Other activities co-organizer of the minisymposium "Limit behavior and asymptotic properties in fluid mechanics" at ICIAM 2023 (August 20–25, 2023) co-organizer of the Seminar "Material Modeling" at WIAS co-organizer of the Young Researchers' Forum on Mathematical Fluid Mechanics (June 20 & 21, 2022) co-organizer of the minisymposium "Recent Developments in the Mathematical Analysis of Viscous Fluids" at SIAM PD22 (March 14–18, 2022)

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

Publications and preprints

1. T. Eiter, Y. Shibata.
   Viscous flow past a translating body with oscillating boundary.
   Preprint.  arXiv:2303.09592  WIAS Preprint No. 3000.
2. T. Eiter, R. Lasarzik.
   Existence of energy-variational solutions to hyperbolic conservation laws.
   Preprint.  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.
   Preprint.  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, 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.
15. 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.
16. 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]

Thesis

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

Short CV

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

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Last modified: 2023-07-26 by Thomas Eiter