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

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

 

Scientific, academic and artistic work

Displaying a selection of activities. See all publications in the database

Journal publications