Focus of Research
- theory of nonlinear partial differential equations
- fluid dynamics
- transport, turbulence and mixing
- degenerate and singular parabolic equations
- regularity theory
Publications
- . Steady ring-shaped vortex sheets arXiv.org. [submitted / under review]
- .. Strong convergence of vorticities in the 2D viscosity limit on a bounded domain ArXiv.org. [submitted / under review]
- .. ‘Optimal Regularity for the 2D Euler Equations in the Yudovich class.’ Journal de Mathématiques Pures et Appliquées . [accepted / in Press (not yet published)]
- . . ‘Propagation of regularity for transport equations. A Littlewood-Paley approach.’ Indiana University Mathematics Journal 73, № 2: 445–473.
- . . ‘On the dynamics of vortices in viscous 2D flows.’ Mathematische Annalen 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
- . . ‘Invariant Manifolds for the Thin Film Equation.’ Archive for Rational Mechanics and Analysis 248, № 2. doi: 10.1007/s00205-024-01968-y.
- . . ‘Finite-dimensional leading order dynamics for the fast diffusion equation near extinction.’ Discrete and Continuous Dynamical Systems - Series A 44, № 9: 2697–2712. doi: 10.3934/dcds.2024043.
- . . ‘Fine large-time asymptotics for the axisymmetric Navier-Stokes equations.’ Journal of Evolution Equations 24: 72. doi: 10.1007/s00028-024-01001-5.
- . Stability of traveling waves for doubly nonlinear equations arXiv.org. [submitted / under review]
- . . ‘Asymptotics near extinction for nonlinear fast diffusion on a bounded domain.’ Archive for Rational Mechanics and Analysis 247: 16. doi: 10.1007/s00205-023-01850-3.
- . . ‘Optimal regularity of isoperimetric sets with Hölder densities.’ Calculus of Variations and Partial Differential Equations 62, № 214. doi: 10.1007/s00526-023-02542-2.
- . . ‘The Scharfetter-Gummel scheme for aggregation-diffusion equations.’ IMA Journal of Numerical Analysis 42, № 3. doi: 10.1093/imanum/drab039.
- . . ‘Bounds on the rate of enhanced dissipation.’ Communications in Mathematical Physics Online first. doi: 10.1007/s00220-022-04588-3.
- . . ‘Renormalization and energy conservation for axisymmetry fluid flows.’ Mathematische Annalen 382: 1–36. doi: 10.1007/s00208-020-02050-0.
- . . ‘Optimal stability estimates and a new uniqueness result for advection-diffusion equations.’ Pure and Applied Analysis 4, № 3: 571–596. doi: 10.2140/paa.2022.4.571.
- . . ‘On the dynamics of point vortices for the 2D Euler equation with Lp vorticity.’ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, № 2226. doi: 10.1098/rsta.2021.0046.
- . . ‘A note on the vanishing viscosity limit in the Yudovich class.’ Canadian Mathematical Bulletin 64, № 1: 112–122. doi: 10.4153/S0008439520000296.
- . . ‘Vortex dynamics for 2D Euler flows with unbounded vorticity.’ Revista Matematica Iberoamericana 37, № 5: 1969–1990. doi: 10.4171/rmi/1255.
- . . ‘On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity.’ Nonlinearity 34, № 5: 3112–3121. doi: 10.1088/1361-6544/abe51f.
- . . ‘A well-posedness result for a system of cross-diffusion equations.’ Journal of Evolution Equations 21, № 2: 2471–2489. doi: 10.1007/s00028-021-00690-6.
- . . ‘On the Littlewood-Paley spectrum for passive scalar transport equations.’ Journal of Nonlinear Science 30, № 2: 645–656. doi: 10.1007/s00332-019-09585-w.
- . . ‘Optimal stability estimates for continuity equations.’ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, № A: 1279–1296. doi: 10.1017/S0308210518000173.
- . . ‘The thin film equation close to self-similarity.’ Analysis and PDE 11, № 5: 1303–1342. doi: 10.2140/apde.2018.11.1303.
- . ‘Analysis of the implicit upwind finite volume scheme with rough coefficients.’ Numerische Mathematik 139, № 1: 155–186. doi: 10.1007/s00211-017-0935-1.
- . ‘On the Vortex Filament Conjecture for Euler Flows.’ Archive for Rational Mechanics and Analysis 224, № 1: 135–172. doi: 10.1007/s00205-016-1070-3.
- . ‘Convergence rates for upwind schemes with rough coefficients.’ SIAM Journal on Numerical Analysis 55, № 2: 812–840. doi: 10.1137/16M1084882.
- . . ‘Eulerian and Lagrangian solutions to the continuity and Euler equations with $L^1$ vorticity.’ SIAM Journal on Mathematical Analysis 49, № 5: 3973–3998. doi: 10.1137/17M1130988.
- . . ‘Optimal stability estimates for continuity equations.’ Oberwolfach Reports 14, № 1. doi: 10.4171/OWR/2017/7.
- . ‘A quantitative theory for the continuity equation.’ Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 34, № 7: 1837–1850. doi: 10.1016/j.anihpc.2017.01.001.
- . ‘Global solutions to the volume-preserving mean-curvature flow.’ Calculus of Variations and Partial Differential Equations 55, № 1: 1–23. doi: 10.1007/s00526-015-0943-x.
- . ‘An elementary approach to linear programming duality with application to capacity constrained transport.’ Journal of Convex Analysis 22, № 3: 797–808.
- . ‘Scaling bounds on dissipation in turbulent flows.’ Journal of Fluid Mechanics 777: 591–603. doi: 10.1017/jfm.2015.384.
- . ‘The Spectrum of a Family of Fourth-Order Nonlinear Diffusions Near the Global Attractor.’ Communications in Partial Differential Equations 40, № 2: 191–218. doi: 10.1080/03605302.2014.963605.
- . ‘Dual potentials for capacity constrained optimal transport.’ Calculus of Variations and Partial Differential Equations 54, № 1: 573–584. doi: 10.1007/s00526-014-0795-9.
- . Invariant manifolds for the porous medium equation. [submitted / under review]
- . ‘Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator.’ Journal of Differential Equations 256, № 3: 1191–1223. doi: 10.1016/j.jde.2013.10.013.
- . ‘Crossover of the coarsening rates in demixing of binary viscous liquids.’ Communications in Mathematical Sciences 11, № 2: 441–464.
- . ‘Maximal mixing by incompressible fluid flows.’ Nonlinearity 26, № 12: 3279–3289. doi: 10.1088/0951-7715/26/12/3279.
- . ‘Laminar Boundary Layers in Convective Heat Transport.’ Communications in Mathematical Physics 324, № 3: 995–1031. doi: 10.1007/s00220-013-1826-7.
- . . ‘On the coarsening rates for attachment-limited kinetics.’ SIAM Journal on Mathematical Analysis 45, № 1: 324–344. doi: 10.1137/120865197.
- . ‘Rayleigh-Bénard convection: Improved bounds on the Nusselt number.’ Journal of Mathematical Physics 52, № 8. doi: 10.1063/1.3623417.
- . . ‘On the coarsening rates in demixing binary viscous liquids.’ Oberwolfach Reports 8, № 4. doi: 10.4171/OWR/2011/55.
- . . Scaling laws in two models for thermodynamically driven fluid flows Dissertation thesis, Universität Leipzig. Leipzig.
- . . ‘Upper bounds on coarsening rates in demixing binary viscous liquids.’ SIAM Journal on Mathematical Analysis 43, № 1: 134. doi: 10.1137/090775142.
Projects
- EXC 2044 - C1: Evolution and asymptotics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C2: Multi-scale phenomena and macroscopic structures ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - Mathematical analysis of bubble rings in ideal fluids ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: SE 2436/5-1 - Transport Equations, mixing and fluid dynamics ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: SE 2436/3-1 - Invariante Mannigfaltigkeiten für schnelle Diffusionen nahe Auslöschung ( – )
Individual Granted Project: DFG - Individual Grants Programme | Project Number: SE 2436/4-1
- EXC 2044 - C1: Evolution and asymptotics ( – )
Events
2024 Minisymposium on recent developments in mathematical fluid dynamics during the Equadiff in Karlstad, jointly with Michele Coti Zelati.
2023 Co-organizer of the Workshop on Mixing, Stability and Fluid Dynamics (zusammen mit V. Navarro-Fernández und A. Schlichting) in Münster.
2021 Co-organizer of the Workshop New Trends in Geometric PDEs (jointly with C. Boehm, G. Holzegel and B. Wilking) at the WWU. This Workshop is part of the focus programme Geometry and PDEs: From Theory to Applications.
2019 Co-organizer of the 5th Applied Mathematics Symposium Münster Transport, Mixing and Fluids (jointly with E. Wiedemann) at the WWU.
2015 Co-organizer of the Hausdorff School Nonlinear evolutions: Kinetic equations and defect dynamics (jointly with B. Niethammer and J.J.L. Velázquez) at the am Hausdorff Center in Bonn.