Junior Research Group Vortices and nonlinear waves
The junior research group Vortices and nonlinear waves is led by Lars Eric Hientzsch while being funded by the CRC1173 on Wave Phenomena where it is represented by the associated project AP9.
Research activities
Its research activities concern the mathematical analysis of nonlinear PDEs arising in the description of quantum and geophysical fluid flow, often related to the propagation and interaction of waves.
The research develops along two main directions
- (quantised) vortices and nonlinear waves,
- hydrodynamic stability and regularity properties of geophysical fluid flow.
These research lines share a common file rouge given by the investigation of coherent structures. Specifically, we are interested in the properties (quantised) vortices, vortex filaments and the characterisation of related asymptotic dynamics.
Quantized vortices and nonlinear waves
A quantum fluid is a system of interacting particles that exhibits effects of quantum statistics also at a macroscopic scale such as for superfluidity, Bose-Einstein condensation and electron transport in semiconductors. The prototype model is the so called Quantum Hydrodynamic system (QHD) describing an inviscid compressible fluid flow featuring a dispersive tensor accounting for the quantum effects. From a mathematical perspective, the QHD system reads as a compressible Euler system augmented by a dispersive stress tensor figuring as quantum correction.
With a hybrid approach relying on both dispersive PDEs and fluid mechanical models and techniques, we investigate the Cauchy theory for these systems and relevant physical phenoemna such as the occurence of quantized vortices.
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Hydrodynamic (in-)stability of geophysical fluid flow
A fundamental question for the understanding of hydrodynamic stability consists in rigorously describing the dynamics of vortices and vortex filaments in incompressible fluids. The vortex filament conjecture states that initial concentration around such a curve persists and the curve evolves through the binormal curvature flow. In its generality, the conjecture remains unsolved and the evolution and interaction of vortex filaments in incompressible fluids remains a puzzling problem. Vortex solutions are of low regularity and as such fall in general outside the usual well-posedness framework.
We derive and analyse the relevant asymptotic dynamics in contexts with spatial heterogeneities such as the (degenerate) lake equations describing a 2D fluid with prescribed but varying topography and the 3D axisymmetric Euler eeqeuations.
A parallel research concerns ill-posedness phenomena and instabilities in models for geophysical fluid mechanics such as the (stratified) Boussinesq equations caputered by a careful analysis of the interaction of nonlinear waves.
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Recent publications
| 2 | M. Caggio, L.E. Hientzsch, D. Donatelli, Inviscid incompressible limit for capillary fluids with density dependent viscosity, arXived as arXiv:2507.00621 (2025) |
| 1 | M. Donati, L.E. Hientzsch, C. Lacave, E. Miot, On the dynamics of leapfrogging vortex rings, arXived as arXiv:2503.21604 (2025) |
Staff in the junior research group
| Name | Tel. | |
| Dr. Lars Eric Hientzsch | +49 721 608 43038 | lars.hientzsch@kit.edu |
Recent guests of the junior research group
| July 2025 | Dr. Clara Patriarca | Talk |
| June 2025 | Dr. Raffaele Scandone | Talk |
| June 2025 | Dr. Frederic Valet | Talk |
| May 2025 | Jordan Berthoumieu |