Background and activities
Nonlinear partial differential equations
Elliptic equations; primarily stationary free-boundary flows. I have also done some work on ordinary differential, integro-differential and difference equations.
Of particular interest are travelling water waves, free-surface flows and rotational currents. Current foci are waves with critical layers, multimodal waves and Whitham-like equations.
Current research group
Gabriele Brüll (Postdoc), Yuexun Wang (Postdoc); Long Pei (PhD), Mathias Nikolai Arnesen (PhD), Kristoffer Varholm (PhD), Filippo Remonato (PhD), Fredrik Hildrum (PhD).
Current projects and programmes
- Principal investigator of the NRC-project Nonlinear Water Waves, 2014–2017.
- Project leader for the educational project Kvalitet, tilgjengelighet og differensiering i grunnutdanningen i Matematikk (KTDiM), NTNU, 2014–2016.
- Participant in the Outstanding Academic Fellows research programme for excellence, NTNU, 2014–2017.
CV available for download above.
Scientific, academic and artistic work
Displaying a selection of activities. See all publications in the database
- (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberwolfach Reports.
- (2015) A note on the local well-posedness for the whitham equation. Springer Proceedings in Mathematics. vol. 119.
- (2014) Trimodal Steady Water Waves. Archive for Rational Mechanics and Analysis.
- (2013) Steady-state fingering patterns for a periodic Muskat problem. Methods and Applications of Analysis. vol. 20 (1).
- (2013) Global bifurcation for the Whitham equation. Mathematical Modelling of Natural Phenomena. vol. 8 (5).
- (2012) On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type. Nonlinearity. vol. 25 (10).
- (2011) Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell. Journal of Mathematical Fluid Mechanics. vol. 13.
- (2011) Steady water waves with multiple critical layers: interior dynamics. Journal of Mathematical Fluid Mechanics. vol. 14.
- (2011) Steady water waves with multiple critical layers. SIAM Journal on Mathematical Analysis. vol. 43.
- (2011) Asymptotic integration of second order nonlinear difference equations. Glasgow Mathematical Journal. vol. 53.
- (2016) A presentation of the mathematical theory for the highest wave of the Whitham equation in connection to the awarding of the Wallenberg prize 2016. Svenska Matematikersamfundets årsmöte ; 2016-06-17.
- (2016) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberseminar Analysis und Physik ; Leibniz Universität Hannover. 2016-02-01.
- (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop on Interactions between Partial Differential Equations and Functional Inequalities (Institut Mittag-Leffler) ; Stockholm. 2016-09-12 - 2016-09-16.
- (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop ”Recent progress on the qualitative properties of nonlinear dispersive equations and systems” (Wolfgang Pauli Institute) ; 2016-09-19 - 2016-09-23.
- (2016) Symmetry and decay properties of traveling wave solutions to the Whitham equation. Differential Equations Seminar ; University of Missouri. 2016-12-03.
- (2015) Multi-dimensional bifurcation of steady water waves with vorticity. SIAM Conference on Analysis of Partial Differential Equations ; 2015-12-06 - 2016-12-10.
- (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Online seminar on Applied Partial Differential Equations (University of Washington) ; 2015-10-15.