Background and activities
Main field: Nonlinear partial differential equations arising in fluid mechanics
Most works on the Euler equations concern travelling waves upon rotational currents, with critical layers. My current focus is mainly on fully — or very weakly — dispersive nonlinear equations of nonlocal type, such as the Whitham equation and its siblings. Here, questions about the existence and regularity of so-called highest waves, solitary waves, as well as existence times in the evolutionary problem are particularly intriguing.
Current research group
Yuexun Wang (Postdoc), Mathias Nikolai Arnesen (Postdoc), Dag Nilsson (Postdoc), Kristoffer Varholm (PhD), Fredrik Hildrum (PhD), Ola Isaac Høgåsen Mæhlen (PhD).
Current projects and programmes
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016–2020.
I am a member of the The Royal Norwegian Society of Sciences and Letters. CV available for download above.
Preprints and online first
- M. Ehrnström, M. A. Johnson, O. I. H. Maehlen, F. Remonato. On the bifurcation diagram of the capillary-gravity Whitham equation. arxiv:1901.03534
- M. Ehrnström and Y. Wang. Enhanced existence time of solutions to the fractional Korteweg-de Vries equation. arxiv:1804.06297
- M. Ehrnström and E. Wahlén. On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Accepted for publication in Ann. Inst. H. Poincaré Anal. Non. Linéaire (2018). 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
Journal publications
- (2018) Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Nonlinearity. vol. 31 (12).
- (2018) Existence of a Highest Wave in a Fully Dispersive Two-Way Shallow Water Model. Archive for Rational Mechanics and Analysis. vol. 231.
- (2018) Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces. Journal of evolution equations (Printed ed.). vol. 18 (3).
- (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.