Mats Ehrnstrom
About
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
Kristoffer Varholm (Postdoc), Yuya Suzuki (Postdoc), Douglas Svensson Seth (Postdoc), Fredrik Hildrum (PhD), Jun Xue (PhD).
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
Publications
2019
- Ehrnstrom, Mats; Remonato, Filippo; Mæhlen, Ola Isaac Høgåsen; Johnson, Mathew A. (2019) On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation. Water Waves. volum 1.
- Ehrnstrom, Mats; Wahlén, Erik. (2019) On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation. Annales de l'Institut Henri Poincare. Analyse non linéar. volum 36 (6).
- Ehrnstrom, Mats; Wang, Yuexun. (2019) Enhanced existence time of solutions to the fractional Korteweg de Vries equation. SIAM Journal on Mathematical Analysis. volum 51 (4).
2018
- Ehrnstrom, Mats; Groves, Mark D. (2018) Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Nonlinearity. volum 31 (12).
- Ehrnstrom, Mats; Johnson, Mathew A; Claassen, Kyle M. (2018) Existence of a Highest Wave in a Fully Dispersive Two-Way Shallow Water Model. Archive for Rational Mechanics and Analysis. volum 231.
- Ehrnstrom, Mats; Pei, Long. (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.). volum 18 (3).
2017
- Bruell, Gabriele; Ehrnstrom, Mats; Geyer, Anna; Pei, Long. (2017) Symmetric solutions of evolutionary partial differential equations. Nonlinearity. volum 30 (10).
- Brüll, Gabriele; Ehrnstrom, Mats; Pei, Long. (2017) Symmetry and decay of traveling wave solutions to the Whitham equation. Journal of Differential Equations. volum 262 (8).
2015
- Ehrnstrom, Mats. (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberwolfach Reports.
- Ehrnstrom, Mats; Escher, Joachim; Pei, Long. (2015) A note on the local well-posedness for the whitham equation. Springer Proceedings in Mathematics. volum 119.
2014
- Ehrnström, Mats Harald Andreas; Wahlén, E.. (2014) Trimodal Steady Water Waves. Archive for Rational Mechanics and Analysis.
2013
- Ehrnström, Mats Harald Andreas; Escher, Joachim; Matioc, Bogdan-Vasile. (2013) Steady-state fingering patterns for a periodic Muskat problem. Methods and Applications of Analysis. volum 20 (1).
- Ehrnström, Mats Harald Andreas; Kalisch, Henrik. (2013) Global bifurcation for the Whitham equation. Mathematical Modelling of Natural Phenomena. volum 8 (5).
2012
- Ehrnström, Mats Harald Andreas; Groves, Mark; Wahlén, E.. (2012) On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type. Nonlinearity. volum 25 (10).
2011
- Ehrnström, Mats; Escher, J.; Matioc, B.-V.. (2011) Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell. Journal of Mathematical Fluid Mechanics. volum 13.
- Ehrnström, Mats; Escher, J.; Villari, G.. (2011) Steady water waves with multiple critical layers: interior dynamics. Journal of Mathematical Fluid Mechanics. volum 14.
- Ehrnström, Mats; Escher, J.; Wahlén, E.. (2011) Steady water waves with multiple critical layers. SIAM Journal on Mathematical Analysis. volum 43.
- Ehrnström, Mats; Tisdell, C.C.; Wahlén, E.. (2011) Asymptotic integration of second order nonlinear difference equations. Glasgow Mathematical Journal. volum 53.
Journal publications
- Ehrnstrom, Mats; Remonato, Filippo; Mæhlen, Ola Isaac Høgåsen; Johnson, Mathew A. (2019) On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation. Water Waves. volum 1.
- Ehrnstrom, Mats; Wahlén, Erik. (2019) On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation. Annales de l'Institut Henri Poincare. Analyse non linéar. volum 36 (6).
- Ehrnstrom, Mats; Wang, Yuexun. (2019) Enhanced existence time of solutions to the fractional Korteweg de Vries equation. SIAM Journal on Mathematical Analysis. volum 51 (4).
- Ehrnstrom, Mats; Groves, Mark D. (2018) Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Nonlinearity. volum 31 (12).
- Ehrnstrom, Mats; Johnson, Mathew A; Claassen, Kyle M. (2018) Existence of a Highest Wave in a Fully Dispersive Two-Way Shallow Water Model. Archive for Rational Mechanics and Analysis. volum 231.
- Ehrnstrom, Mats; Pei, Long. (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.). volum 18 (3).
- Bruell, Gabriele; Ehrnstrom, Mats; Geyer, Anna; Pei, Long. (2017) Symmetric solutions of evolutionary partial differential equations. Nonlinearity. volum 30 (10).
- Brüll, Gabriele; Ehrnstrom, Mats; Pei, Long. (2017) Symmetry and decay of traveling wave solutions to the Whitham equation. Journal of Differential Equations. volum 262 (8).
- Ehrnstrom, Mats. (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberwolfach Reports.
- Ehrnstrom, Mats; Escher, Joachim; Pei, Long. (2015) A note on the local well-posedness for the whitham equation. Springer Proceedings in Mathematics. volum 119.
- Ehrnström, Mats Harald Andreas; Wahlén, E.. (2014) Trimodal Steady Water Waves. Archive for Rational Mechanics and Analysis.
- Ehrnström, Mats Harald Andreas; Escher, Joachim; Matioc, Bogdan-Vasile. (2013) Steady-state fingering patterns for a periodic Muskat problem. Methods and Applications of Analysis. volum 20 (1).
- Ehrnström, Mats Harald Andreas; Kalisch, Henrik. (2013) Global bifurcation for the Whitham equation. Mathematical Modelling of Natural Phenomena. volum 8 (5).
- Ehrnström, Mats Harald Andreas; Groves, Mark; Wahlén, E.. (2012) On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type. Nonlinearity. volum 25 (10).
- Ehrnström, Mats; Escher, J.; Matioc, B.-V.. (2011) Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell. Journal of Mathematical Fluid Mechanics. volum 13.
- Ehrnström, Mats; Escher, J.; Villari, G.. (2011) Steady water waves with multiple critical layers: interior dynamics. Journal of Mathematical Fluid Mechanics. volum 14.
- Ehrnström, Mats; Escher, J.; Wahlén, E.. (2011) Steady water waves with multiple critical layers. SIAM Journal on Mathematical Analysis. volum 43.
- Ehrnström, Mats; Tisdell, C.C.; Wahlén, E.. (2011) Asymptotic integration of second order nonlinear difference equations. Glasgow Mathematical Journal. volum 53.