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Photo of Christian Zillinger

PD Dr. Christian Zillinger

  • Englerstrasse 2
    76131 Karlsruhe
    Germany

You can find information about my project "Stability and Instability in Fluids and Materials" (AP6) in the CRC 1173 on its project page and here.

Current List of Courses
Semester Titel Typ
Winter Semester 2023/24 Lecture
Summer Semester 2022 Lecture
Winter Semester 2021/22 Lecture
Winter Semester 2020/21 Seminar

Research

My research interests are in partial differential equations motivated by physical problems in particular fluid dynamics and material sciences and include:

  • Mixing as a (de)stabilizing mechanism in fluids and inviscid damping.
  • Cascades of resonances and instabilities in fluids and plasmas.
  • Convex integration and microstructures in materials. Rigidity and flexibility.
  • Magnetic fluids.
  • Partial dissipation in the Boussinesq equations.

Publications

  1. (with Niklas Knobel) On Echoes in Magnetohydrodynamics with Magnetic Dissipation, Journal of Differential Equations, Volume 367, 15 September 2023, Pages 625-688, 2023.
  2. On stability estimates for the inviscid Boussinesq equations, Journal of Nonlinear Science, 33, Article number: 106 (2023), 2023.
  3. (with Xian Liao) On variable viscosity and enhanced dissipation, Nonlinearity, Volume 36, Number 11, 2023.
  4. On echo chains in the linearized Boussinesq equations around traveling waves, SIAM Journal on Mathematical Analysis, Vol. 55, Iss. 5 (2023), 2023.
  5. On the Boussinesq Equations with Non-monotone Temperature Profiles, Journal of Nonlinear Science volume 31, Article number: 64 (2021), 2021.
  6. (with Francesco Della Porta, Angkana Rüland, Jamie Taylor) On a probabilistic model for martensitic avalanches incorporating mechanical compatibility, Nonlinearity 34.7 (2021): 4844, 2021.
  7. On Enhanced Dissipation for the Boussinesq Equations, Journal of Differential Equations, Volume 282, Pages 407-445, 2021.
  8. On Echo Chains in Landau Damping: Traveling Wave-like Solutions and Gevrey 3 as a Linear Stability Threshold, Annals of PDE 7, 1 (2021), 2021.
  9. (with Yu Deng) Echo chains as a linear mechanism: Norm inflation, modified exponents and asymptotics, Archive for Rational Mechanics and Analysis 242(1), 643-700, 2021.
  10. (with Yu Deng) On the Smallness Condition in Linear Inviscid Damping:Monotonicity and Resonance Chains, Nonlinearity 33 6176, 2020.
  11. Linear Inviscid Damping in Sobolev and Gevrey Spaces, Nonlinear Analysis 213 (2021): 112492, 2021.
  12. (with Angkana Rüland, Barbara Zwicknagl) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Planar Geometrically Linearized Hexagonal-to-Rhombic Phase Transformation, Journal of Elasticity (2019): 1-76, 2019.
  13. (with Pierluigi Cesana, Francesco Della Porta, Angkana Rüland, Barbara Zwicknagl) Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers, Arch. Rational Mech. Anal. 237 (2020) 383–445, 2020.
  14. (with Michele Coti Zelati) On degenerate circular and shear flows: the point vortex and power law circular flows, Communications in Partial Differential Equations, 44:2,110-155, 2019.
  15. On the forced Euler and Navier-Stokes equations: linear damping and modified scattering, Journal of Mathematical Fluid Mechanics(2019) 21:49, 2019.
  16. On geometric and analytic mixing scales: comparability and convergence rates for transport problems, Pure and Applied Analysis 1.4 (2019): 543-570, 2019.
  17. (with Angkana Rüland, Jamie M Taylor) Convex integration arising in the modelling of shape-memory alloys: rigidity, flexibility and some numerical implementations, Journal of Nonlinear Science 29, p. 2137–2184 (2019), 2019.
  18. (with Angkana Rüland, Barbara Zwicknagl) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc), SIAM J. Math. Anal., 50(4), 3791–3841, 2018.
  19. On circular flows: linear stability and damping, J. Differential Equations 263, 7856–7899, 2017.
  20. Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity, Archive for Rational Mechanics and Analysis, 221(3):1449-1509, 2016.
  21. Linear inviscid damping for monotone shear flows, Transactions of the AMS, 369, 8799–8855, 2016.

You can also find a list of my publications on the arxiv, in my google scholar profile and in my OrcId profile.


Preprints

  1. On nonlinear Landau damping and Gevrey regularity, arXiv preprint 2307.14271, 2023.
  2. (with Niklas Knobel) On the Sobolev Stability Threshold for the 2D MHD Equations with Horizontal Magnetic Dissipation, arXiv preprint 2309.00496, 2023

Proceedings

  1. On Resonance Chains in the Boussinesq Equations, Oberwolfach Report, 2023

Habilitation thesis

  1. On Mixing and Resonances in Fluid Systems, KIT, 2023

I obtained my PhD under the supervision of Herbert Koch at the University of Bonn and have been an assistant professor (NTT) at the University of Southern California and a postdoctoral fellow at BCAM.