Prof. Dr. Klaus Widmayer

Vita

Education

• PhD, Courant Institute, New York University, 2016

Employment

• Tamarkin Assistant Professor, Brown University, 2016-2017
• Research Scientist and Lecturer, EPFL, 2017-2022
• Assistant Professor (SNF Eccellenza Professorial Fellowship), University of Zurich, 2022-present
• Assistant Professor, University of Vienna, 2022-present

Forschung

My research is centered on questions of stability and asymptotic behavior in evolution 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 [2,3,4,5,12,14,18,20] 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 [7,9,11,18] 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 below [8,13] on vacuum, [10,16] on a repulsive point charge, and [15,17,19] on spatially homogeneous configurations ("Landau damping").

Publications and Preprints

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

1. On the stability of vacuum in the screened Vlasov-Poisson equation [arXiv:2410.17978]
   -- with Mikaela Iacobelli, Stefano Rossi
   arXiv preprint 2024
2. Long-time stability of a stably stratified rest state in the inviscid 2D Boussinesq equation [arXiv:2408.15154]
   -- with Catalina Jurja
   arXiv preprint 2024
3. Nonlinear Landau damping and wave operators in sharp Gevrey spaces [arXiv:2405.04473]
   -- with Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang
   arXiv preprint 2024
4. Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing [arXiv:2402.15312]
   -- with Michele Coti Zelati, Augusto Del Zotto
   arXiv preprint 2024
5. On the stability of homogeneous equilibria in the Vlasov-Poisson system on R^3 [arXiv:2305.11166]
   -- with Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang
   Class. Quantum Grav. 40 (2023) 185007
6. Stability of a point charge for the repulsive Vlasov-Poisson system [arXiv:2207.05644]
   -- with Benoit Pausader, Jiaqi Yang
   J. Eur. Math. Soc., to appear
7. 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
   Annals of PDE 10, 2 (2024)
8. Global Axisymmetric Euler Flows with Rotation [arXiv:2109.01029]
   -- with Yan Guo, Benoit Pausader
   Inventiones Mathematicae 231, pages 169–262 (2023)
9. Scattering map for the Vlasov-Poisson system [arXiv:2101.01390]
   -- with Patrick Flynn, Zhimeng Ouyang, Benoit Pausader
   Peking Mathematical Journal 6, 365-392 (2023)
10. 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., Volume 76, Issue 12, December 2023, 3553-3641
11. Mixing and diffusion for rough shear flows [arXiv:2009.12268]
    -- with Maria Colombo, Michele Coti Zelati
    Ars Inveniendi Analytica, Paper No. 2 (2021)
12. 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)
13. Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations [arXiv:2007.11547]
    -- with Michele Coti Zelati, Tarek M. Elgindi
    Archive for Rational Mechanics and Analysis 247, 12 (2023)
14. 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
15. 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)
16. 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
17. On the Global Stability of a Beta-Plane Equation [arXiv:1610.03479]
    -- with Fabio Pusateri
    Analysis & PDE, Vol. 11 (2018), No. 7, 1587-1624
18. Convergence to Stratified Flow for an Inviscid 3D Boussinesq System [arXiv:1509.09216]
    Commun. Math. Sci. Vol. 16, No. 6, pp. 1713-1728
19. 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
20. 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
21. 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