Forschung
Forschungsschwerpunkte
- Theorie nichtlinearer partieller Differentialgleichungen
- Fluiddynamik
- Transport, Turbulenz und Mischungen
- Poröse Medien und dünne Filme
- Numerische Analysis
Publikationen
- . . ‘A scattering theory construction of dynamical vacuum black holes.’ Journal of Differential Geometry 126, Nr. 2: 633–740. doi: 10.4310/jdg/1712344221.
- . . ‘Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.’ Classical and Quantum Gravity 40, Nr. 4. doi: 10.1088/1361-6382/acb0ac.
- . The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms arXiv. doi: 10.48550/arXiv.2302.06387.
- . . ‘The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes.’ Archive for Rational Mechanics and Analysis 247: 56. doi: 10.1007/s00205-023-01890-9.
- . Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes arXiv. doi: 10.48550/arXiv.2212.14093.
- . The non-linear stability of the Schwarzschild family of black holes arXiv. doi: 10.48550/arXiv.2104.08222.
- . . ‘Asymptotic properties of linear field equations in anti-de Sitter space.’ Communications in Mathematical Physics 374: 1125–1178. doi: 10.1007/s00220-019-03601-6.
- . A note on the wave equation on black hole spacetimes with small non-decaying first order terms arXiv. doi: 10.48550/arXiv.2005.13644.
- . . ‘Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M.’ Annals of PDE 5, Nr. 2: 1–118. doi: 10.1007/s40818-018-0058-8.
- . . ‘The linear stability of the Schwarzschild solution to gravitational perturbations.’ Acta Mathematica 222, Nr. 1: 1–214. doi: 10.4310/ACTA.2019.v222.n1.a1.
- . . ‘Unique continuation from infinity in asymptotically anti-de Sitter spacetimes II: Non-static boundaries.’ Communications in Partial Differential Equations 42, Nr. 12: 1871–1922. doi: 10.1080/03605302.2017.1390677.
- . . ‘Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric.’ Classical and Quantum Gravity 33, Nr. 20: 205004. doi: 10.1088/0264-9381/33/20/205004.
- . . ‘Small-data shock formation in solutions to 3D quasilinear wave equations: An overview.’ Journal of Hyperbolic Differential Equations 13, Nr. 1: 1–105. doi: 10.1142/S0219891616500016.
- . . ‘Unique continuation from infinity in asymptotically anti-de Sitter spacetimes.’ Communications in Mathematical Physics 347: 723–775. doi: 10.1007/s00220-016-2576-0.
- . . ‘The Einstein–Klein–Gordon–AdS system for general boundary conditions.’ Journal of Hyperbolic Differential Equations 12, Nr. 2: 293–342. doi: 10.1142/S0219891615500095.
- . . ‘Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes.’ Journal of Functional Analysis 226, Nr. 4: 2436–2485. doi: 10.1016/j.jfa.2013.10.019.
- . . ‘Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes.’ Analysis and PDE 7, Nr. 5: 1057–1090. doi: 10.2140/apde.2014.7.1057.
- . . ‘Decay Properties of Klein-Gordon Fields on Kerr-AdS Spacetimes.’ Communications on Pure and Applied Mathematics 66, Nr. 11: 1751–1802. doi: 10.1002/cpa.21470.
- . . ‘Stability of Schwarzschild-AdS for the sphericallysymmetric Einstein-Klein-Gordon system.’ Communications in Mathematical Physics 317: 205–251. doi: 10.1007/s00220-012-1572-2.
- . . ‘Well-posedness for the massive wave equation on asymptotically anti-de Sitter spacetimes.’ Journal of Hyperbolic Differential Equations 9, Nr. 2: 239–261. doi: 10.1142/S0219891612500087.
- . . ‘Self-gravitating Klein–Gordon fields in asymptotically anti-de Sitter spacetimes.’ Annales Henri Poincare 13: 991–1038. doi: 10.1007/s00023-011-0146-8.
- . . ‘On the massive wave equation on slowly rotating Kerr-AdS spacetimes.’ Communications in Mathematical Physics 294: 169–197. doi: 10.1007/s00220-009-0935-9.
- . . ‘Stability and decay rates for the five-dimensional Schwarzschild metric under biaxial perturbations.’ Advances in Theoretical and Mathematical Physics 14, Nr. 5: 1245–1372. doi: 10.4310/ATMP.2010.v14.n5.a1.
- . . ‘Ricci flows connecting Taub–Bolt and Taub–NUT metrics.’ Classical and Quantum Gravity 24, Nr. 24: 6201–6217. doi: 10.1088/0264-9381/24/24/004.
- . . ‘On the nonlinear stability of higher dimensional triaxial Bianchi-{IX} black holes.’ Advances in Theoretical and Mathematical Physics 10, Nr. 4: 503–523. doi: 10.4310/ATMP.2006.v10.n4.a2.
- . . ‘On the instability of Lorentzian Taub–NUT space.’ Classical and Quantum Gravity 23, Nr. 11: 3951–3962. doi: 10.1088/0264-9381/23/11/017.
- . . ‘The positive mass and isoperimetric inequalities for axisymmetric black holes in four and five dimensions.’ Classical and Quantum Gravity 23, Nr. 22: 6459–6478. doi: 10.1088/0264-9381/23/22/022.
Ereignisse
2021 Mitorganisator der Workshops New Trends in Geometric PDEs (zusammen mit C. Boehm, G. Holzegel und B. Wilking) an der WWU. Dieser Workshop ist Teil des Fokusprogramms Geometry and PDEs: From Theory to Applications.
2019 Mitorganisator des 5. Symposiums der Angewandten Mathematik Münster Transport, Mixing and Fluids (zusammen mit E. Wiedemann) an der WWU.
2015 Mitorganisator der Hausdorff-Schule Nonlinear evolutions: Kinetic equations and defect dynamics (zusammen mit B. Niethammer und J.J.L. Velázquez) am Hausdorff-Zentrum in Bonn.