Christian Zillinger

PD Dr. Christian Zillinger is a researcher at the Karlsruhe Institute of Technology (KIT), specifically within the Department of Mathematics. He leads the Junior Research Group "Stability and Instability in Fluids and Materials" (AP6) as part of the CRC 1173. His office is located at Kollegiengebäude Mathematik (20.30), room 2.024 in Karlsruhe, Germany.

Dr. Zillinger obtained his PhD under the supervision of Herbert Koch at the University of Bonn. Following his doctorate, he served as an assistant professor (NTT) at the University of Southern California and was a postdoctoral fellow at BCAM (Basque Center for Applied Mathematics). He recently completed his habilitation thesis titled "On Mixing and Resonances in Fluid Systems" at KIT in 2023.

Dr. Zillinger's research focuses on partial differential equations motivated by physical problems, particularly in fluid dynamics and material sciences. His work encompasses several key areas:

• 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, including rigidity and flexibility phenomena
• Magnetic fluids and magnetohydrodynamics
• Partial dissipation in the Boussinesq equations

His recent publications demonstrate a strong focus on stability and instability phenomena in fluid systems, with particular attention to mathematical analysis of PDEs governing fluid behavior. He has made significant contributions to understanding echo chains, resonance phenomena, and damping mechanisms in various fluid models. His work bridges theoretical mathematics with applications in physics and materials science, often employing advanced analytical techniques to address challenging problems in nonlinear PDEs.

Dr. Zillinger actively teaches courses at KIT, including "Klassische Methoden für partielle Differentialgleichungen" (Classical Methods for Partial Differential Equations), "Introduction to convex integration," "Introduction to Kinetic Equations," and seminars on microstructure in materials and fluid dynamics.

He leads the Junior Research Group "Stability and Instability in Fluids and Materials" which is part of the Collaborative Research Centre (CRC) 1173 at KIT, focusing on wave phenomena. This research group investigates mathematical aspects of stability and instability in physical systems, with applications to fluid dynamics and material science.