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), Raj Dhara (Postdoc); Mathias Nikolai Arnesen (PhD), Kristoffer Varholm (PhD), Filippo Remonato (PhD), Fredrik Hildrum (PhD), Ola Isaac Høgåsen Mæhlen (PhD).
Current projects and programmes
- Principal investigator of the RCN project Nonlinear Water Waves, 2014–2018.
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016–2020.
- Participant in the Outstanding Academic Fellows research programme for excellence, NTNU, 2014–2018.
CV available for download above.
- M. Ehrnström and M.D. Groves. Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev–Petviashvili equation. arxiv:1802.04823
- M. Ehrnström and L. Pei. Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces. arXiv:1709.04713
- M. Ehrnström, L. Pei and Y. Wang. A conditional well-posedness result for the bidirectional Whitham equation. arXiv:1708.04551
- M. Ehrnström, M. A. Johnson and K. M. Claassen. Existence of a highest wave in a fully dispersive two-way shallow water model. arXiv:1610.02603
- M. Ehrnström and E. Wahlén. On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. arXiv:1602.05384
Scientific, academic and artistic work
A selection of recent journal publications, artistic productions, books, including book and report excerpts. See all publications in the database
- (2017) Symmetric solutions of evolutionary partial differential equations. Nonlinearity. vol. 30 (10).
- (2017) Symmetry and decay of traveling wave solutions to the Whitham equation. Journal of Differential Equations. vol. 262 (8).
- (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) Steady water waves with critical layers. SIAM Journal on Applied Mathematics.
- (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.
- (2009) Traveling waves for the Whitham equation. Differential and Integral Equations. vol. 22.
- (2009) Recent progress on particle trajectories in steady water waves. Discrete and Continuous Dynamical Systems. vol. 12.