Associated Project 6 • Stability and instability in fluids and materials

In our research we consider physically motivated problems in partial differential equations, which combine physical effects and interesting mathematical phenomena.
Two particular points of focus here are the role of mixing and resonances in fluids and microstructures in materials.

Publications

1. C. Zillinger. Linear inviscid damping in Sobolev and Gevrey spaces. Nonlinear Anal., 213:112492, December 2021. URL https://doi.org/10.1016/j.na.2021.112492. [preprint] [bibtex]

2. Y. Deng and C. Zillinger. Echo chains as a linear mechanism: norm inflation, modified exponents and asymptotics. Arch. Rational Mech. Anal., 242(1):643–700, October 2021. URL https://doi.org/10.1007/s00205-021-01697-6. [preprint] [bibtex]

3. F. Della Porta, A. Rüland, J. Taylor, and C. Zillinger. On a probabilistic model for martensitic avalanches incorporating mechanical compatibility. Nonlinearity, 34(7):4844–4896, June 2021. URL https://doi.org/10.1088/1361-6544/abfca9. [preprint] [bibtex]

4. C. Zillinger. On enhanced dissipation for the Boussinesq equations. J. Differential Equations, 282:407–445, May 2021. URL https://doi.org/10.1016/j.jde.2021.02.029. [preprint] [bibtex]

5. C. Zillinger. On the Boussinesq equations with non-monotone temperature profiles. J. Nonlinear Sci., 31(4):64, 38, May 2021. URL https://doi.org/10.1007/s00332-021-09723-3. [preprint] [bibtex]

6. C. Zillinger. On echo chains in Landau damping: traveling wave-like solutions and Gevrey 3 as a linear stability threshold. Ann. PDE, 7(1):1–29, January 2021. URL https://doi.org/10.1007/s40818-020-00090-y. [preprint] [bibtex]

7. Y. Deng and C. Zillinger. On the smallness condition in linear inviscid damping: monotonicity and resonance chains. Nonlinearity, 33(11):6176–6194, October 2020. URL https://doi.org/10.1088/1361-6544/aba236. [preprint] [bibtex]

8. P. Cesana, F. Della Porta, A. Rüland, C. Zillinger, and B. Zwicknagl. Exact constructions in the (non-linear) planar theory of elasticity: from elastic crystals to nematic elastomers. Arch. Ration. Mech. Anal., 237(1):383–445, July 2020. URL https://doi.org/10.1007/s00205-020-01511-9. [preprint] [bibtex]

Preprints

9. N. Knobel and C. Zillinger. On echoes in magnetohydrodynamics with magnetic dissipation. CRC 1173 Preprint 2023/5, Karlsruhe Institute of Technology, January 2023. [bibtex]

10. C. Zillinger. On stability estimates for the inviscid Boussinesq equations. CRC 1173 Preprint 2022/72, Karlsruhe Institute of Technology, December 2022. [bibtex]

11. X. Liao and C. Zillinger. On variable viscosity and enhanced dissipation. CRC 1173 Preprint 2022/71, Karlsruhe Institute of Technology, December 2022. [bibtex]

12. C. Zillinger. On echo chains in the linearized Boussinesq equations around traveling waves. CRC 1173 Preprint 2022/70, Karlsruhe Institute of Technology, December 2022. [bibtex]