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
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,S. Walsh and C. Zeng. Smooth stationary water waves with exponentially localized vorticity. 40 pages. arxiv:1907.07335
- M. Ehrnström, M. A. Johnson, O. I. H. Maehlen, F. Remonato. On the bifurcation diagram of the capillary-gravity Whitham equation. Accepted for Publication in Water Waves (2019). 38 pages. arxiv:1901.03534
- M. Ehrnström and Y. Wang. Enhanced existence time of solutions to the fractional Korteweg-de Vries equation. SIAM J. Math. Anal., 51 (2019), pp. 3298–3323. arxiv:1804.06297
- M. Ehrnström and E. Wahlén. On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Ann. Inst. H. Poincaré Anal. Non. Linéaire, 36 (2019), pp. 1603–1637. 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
- (2019) Enhanced existence time of solutions to the fractional korteweg–de vries equation. SIAM Journal on Mathematical Analysis. vol. 51 (4).
- (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. Series A. vol. 12.