Background and activities
Nonlinear and nonlocal dispersive partial differential equations
- Existence and properties of steady water waves with vorticity and critical layers
- Nonlocal model equations of very weak dispersion (Whitham type): global branches of solutions, highest waves and regularity
- Solitary and periodic waves in dispersive model equations and systems
- Enhanced existence time and questions related to blow-up
- Data-driven PDEs in connection to water waves and neuroscience
Current research group
Former members (PhDs and Postdocs): Mathias Nikolai Arnesen, Hung Le, Long Pei, Ola Isaac Høgåsen Mæhlen, Yuexun Wang, Dag Nilsson, Gabriele Brüll, Raj Dhara, Filippo Remonato
Active projects and programmes
- Participant in the RCN Toppforsk project Waves and Nonlinear Phenomena, 2016–2022.
- Leader of the RCN Large-scale interdisciplinary researcher project IMod. Partial differential equations, statistics and data: An interdisciplinary approach to data-based modelling, 2022–2028.
I am a member of the The Royal Norwegian Society of Sciences and Letters, and leader of the Differential Equations and Numerical Analysis (DNA) group. CV available for download above.
Preprints and online first
- M. Ehrnström, K. Nik and C. Walker. A direct construction of a full family of Whitham solitary waves. 16 pages. Accepted for publication in Proc. Amer. Math. Soc. arxiv:2204.03274
- M. Ehrnström, M.D. Groves and D. Nilsson. Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation. 35 pages. arxiv:2110.03971
- M. Ehrnström and Y. Wang. Enhanced existence time of solutions to evolution equations of Whitham type. Accepted for publication in Discrete Contin. Dyn. Syst. (DCDS), 42 (2022), pp. 3841–3860. doi:10.3934/dcds.2022035 arXiv:2008.12722
- M. Ehrnström, S. Walsh and C. Zeng. Smooth stationary water waves with exponentially localized vorticity. Accepted for publication in J.Eur. Math. Soc. (JEMS). 40 pages. arxiv:1907.07335
Scientific, academic and artistic work
Displaying a selection of activities. See all publications in the database
- (2019) On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation. Water Waves. vol. 1.
- (2019) On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation. Annales de l'Institut Henri Poincare. Analyse non linéar. vol. 36 (6).
- (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) 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.