Institute of Mathematics

Person

Prof. Dr. Klaus Widmayer

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

E-Mail:
Phone: +41 44 635 58 64
Fax: +41 44 635 57 05
Office: Y27J22
Field of Research:
Analysis, Partielle Differentialgleichungen
Secretary:
E-Mail:
Phone:
Franziska Robmann

+41 44 635 58 31

Vita

Education

  • PhD, Courant Institute, New York University, 2016

Employment

  • Tamarkin Assistant Professor, Brown University, 2016-2017
  • Research Scientist and Lecturer, EPFL, 2017-2022
  • SNF Eccellenza Professorial Fellowship, UZH, 2022-present

Research

My research is centered on questions of stability and asymptotic behavior in evolutions equations of fluid dynamics and kinetic theory.

In the realm of fluid dynamics, two concepts are at the core of my investigations:

  • Dispersion: In the geophysical context, anisotropic forces due to e.g. gravity or rotation give rise to dispersive effects. These can play an important role in stabilizing a flow (see [2,3,4,5,12,14] below).
  • Mixing: This cascading mechanism is often encountered in question of hydrodynamic stability, and responsible for effects like inviscid damping, enhanced dissipation and meta-stable behavior (see [7,9,11] below).

A slightly exotic effect in a related realm is the improvement due to random diffusion in [6].

In kinetic theory, my work focuses on the stability of equilibria in the Vlasov-Poisson equations (see [8,10,13] below).

Publications and Preprints

The following are also available on my arXiv.org page.

  1. Stability of a point charge for the repulsive Vlasov-Poisson system [arXiv:2207.05644]
    -- with Benoit Pausader, Jiaqi Yang
    arXiv preprint 2022
  2. Nonlinear Landau damping for the Vlasov-Poisson system in R^3: the Poisson equilibrium [arXiv:2205.04540]
    -- with Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang
    arXiv preprint 2022
  3. Global Axisymmetric Euler Flows with Rotation [arXiv:2109.01029]
    -- with Yan Guo, Benoit Pausader
    Inventiones Mathematicae, to appear
  4. Scattering map for the Vlasov-Poisson system [arXiv:2101.01390]
    -- with Patrick Flynn, Zhimeng Ouyang, Benoit Pausader
    Peking Mathematical Journal (2021)
  5. On the stabilizing effect of rotation in the 3d Euler equations [arXiv:2010.10460]
    -- with Yan Guo, Chunyan Huang, Benoit Pausader
    Comm. Pure Appl. Math., to appear
  6. Mixing and diffusion for rough shear flows [arXiv:2009.12268]
    -- with Maria Colombo, Michele Coti Zelati
    Ars Inveniendi Analytica, Paper No. 2 (2021)
  7. Stability of a point charge for the Vlasov-Poisson system: the radial case [arXiv:2008.08013]
    -- with Benoit Pausader
    Communications in Mathematical Physics 385, 1741–1769 (2021)
  8. Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations [arXiv:2007.11547]
    -- with Michele Coti Zelati, Tarek M. Elgindi
    arXiv preprint 2020, submitted
  9. On the asymptotic behavior of solutions to the Vlasov-Poisson system [arXiv:2005.03617]
    -- with Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang
    International Mathematics Research Notices, Volume 2022, Issue 12, June 2022, Pages 8865–8889
  10. Enhanced dissipation in the Navier-Stokes equations near the Poiseuille flow [arXiv:1901.01571]
    -- with Michele Coti Zelati, Tarek M. Elgindi
    Communications in Mathematical Physics 378, 987–1010 (2020)
  11. The Surface Quasi-Geostrophic Equation with Random Diffusion [arXiv:1806.03734]
    -- with Tristan Buckmaster, Andrea Nahmod, Gigliola Staffilani
    International Mathematics Research Notices, Volume 2020, Issue 23, November 2020, Pages 9370–9385
  12. On the Global Stability of a Beta-Plane Equation [arXiv:1610.03479]
    -- with Fabio Pusateri
    Analysis & PDE, Vol. 11 (2018), No. 7, 1587-1624
  13. Convergence to Stratified Flow for an Inviscid 3D Boussinesq System [arXiv:1509.09216]
    Commun. Math. Sci. Vol. 16, No. 6, pp. 1713-1728
  14. Long Time Stability for Solutions of a Beta-Plane Equation [arXiv:1509.05355]
    -- with Tarek M. Elgindi
    Comm. Pure Appl. Math., Volume 70, Issue 8, August 2017, Pages 1425-1471
  15. Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems [arXiv:1410.1415]
    -- with Tarek M. Elgindi
    SIAM Journal on Mathematical Analysis, 47 (6), Pages 4672-4684
  16. Non-uniqueness of Weak Solutions to the Wave Map Problem [arXiv:1310.4419]
    Ann. Inst. H. Poincaré (C) Analyse Non Linéaire, Volume 32, Issue 3, May-June 2015, Pages 519-532
Spring 22

Lecture & Seminar

Research seminars
PDE and Mathematical Physics
Do
16.00-18.00
Peter Hintz, Mikaela Iacobelli, Benjamin Schlein, Klaus Widmayer
 

Guest


2022All
GuestStay
Dr. Michele Coti Zelati, Department of Mathematics, Imperial College London (London)
23.07.22 - 27.07.22Widmayer, Klaus
Prof. Dr. Benoît Pausader, Mathematics Department, Brown University (Providence)
23.07.22 - 27.07.22Widmayer, Klaus
Hugo Come, Département Mathématiques, Université Paris-Saclay (Orsay)
01.06.22 - 30.06.22Widmayer, Klaus
Patrick Flynn, Applied Mathematics, Brown University (Providence)
23.05.22 - 05.06.22Widmayer, Klaus