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), Douglas Svensson Seth (Postdoc), Fredrik Hildrum (Postdoc), Swati Yadav (Postdoc), Jun Xue (PhD), Johanna Ulvedal Marstrander (PhD).
Former members (PhDs and Postdocs): Yuya Suzuki, 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
- 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. CV available for download above.
Preprints and online first
- M. Ehrnström, O. I. H. Mæhlen and K. Varholm. On the precise cusped behaviour of extreme solutions to Whitham-type equations. 30 pages. arxiv:2302.08856
Publications
2022
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society.
volum 151 (3).
Academic article
-
Ehrnstrom, Mats;
Nilsson, Dag;
Groves, Mark D.
(2022)
Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation.
SIAM Journal on Mathematical Analysis.
volum 54 (4).
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A.
volum 42 (8).
Academic article
2020
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2020)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print).
Academic article
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.
Academic article
-
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).
Academic article
-
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).
Academic article
2018
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity.
volum 31 (12).
Academic article
-
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.
Academic article
-
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).
Academic article
2017
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity.
volum 30 (10).
Academic article
-
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).
Academic article
2015
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports.
Academic article
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics.
volum 119.
Academic article
2014
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis.
Academic article
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).
Academic article
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena.
volum 8 (5).
Academic article
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).
Academic article
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.
Academic article
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics.
volum 14.
Academic article
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis.
volum 43.
Academic article
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal.
volum 53.
Academic article
Journal publications
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society.
volum 151 (3).
Academic article
-
Ehrnstrom, Mats;
Nilsson, Dag;
Groves, Mark D.
(2022)
Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation.
SIAM Journal on Mathematical Analysis.
volum 54 (4).
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A.
volum 42 (8).
Academic article
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2020)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print).
Academic article
-
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.
Academic article
-
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).
Academic article
-
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).
Academic article
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity.
volum 31 (12).
Academic article
-
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.
Academic article
-
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).
Academic article
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity.
volum 30 (10).
Academic article
-
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).
Academic article
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports.
Academic article
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics.
volum 119.
Academic article
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis.
Academic article
-
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).
Academic article
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena.
volum 8 (5).
Academic article
-
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).
Academic article
-
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.
Academic article
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics.
volum 14.
Academic article
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis.
volum 43.
Academic article
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal.
volum 53.
Academic article
Media
2022
-
Academic lectureEhrnstrom, Mats. (2022) Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvili equation. Numerical and analytical approaches for nonlinear dispersive PDEs ; University of Burgundy. 2022-06-13 - 2022-06-17.
-
Academic lectureEhrnstrom, Mats. (2022) Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvili equation. 2nd Norwegian meeting on PDEs ; Bergen. 2022-06-08 - 2022-06-10.
-
Academic lectureEhrnstrom, Mats. (2022) On some water wave solutions that have emanated from work with G. Villari. Two Days on Qualitative Theory of Differential Equations A conference in honor of Gabriele Villari ; Università degli Studi di Firenze. 2022-09-30 - 2022-10-01.
-
Academic lectureEhrnstrom, Mats. (2022) Smooth stationary water waves with exponentially localised vorticity. Program on Geometric Aspects of Nonlinear Partial Differential Equations ; Institut Mittag-Leffler, Stockholm. 2022-11-15.
2018
-
Academic lectureEhrnstrom, Mats. (2018) Enhanced existence time of solutions to the fractional Korteweg—de Vries equation. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications Dynamics of fluids and nonlinear waves ; Taipei. 2018-07-08 - 2018-07-08.
-
Academic lectureEhrnstrom, Mats. (2018) Enhanced existence time of solutions to the fractional Korteweg—de Vries equation. One-day seminar on Geometry, Analysis and PDEs ; Bergen. 2018-10-22 - 2018-10-22.
-
Academic lectureEhrnstrom, Mats. (2018) On waves of greatest height in fully dispersive nonlocal wave equations. PDE seminar ; University of Warsaw. 2018-03-22 - 2018-03-22.
-
Academic lectureEhrnstrom, Mats. (2018) Travelling water waves with localised vorticity. National meeting of mathematicians . NMF; Bergen. 2018-09-14 - 2018-09-14.
2017
-
LectureBruell, Gabriele; Ehrnstrom, Mats; Pei, Long. (2017) On symmetry and decay of travelling solutions to a nonlocal dispersive equation. Nonlinear Evolution Equations/Wave Phenomena ; 2017-03-28 - 2017-03-31.
-
LectureBruell, Gabriele; Pei, Long; Ehrnstrom, Mats. (2017) On symmetry and decay of travelling wave solutions to a nonlocal dispersive equation. Analysis Seminar, TU Delft ; 2017-05-04 - 2017-05-04.
-
LectureBruell, Gabriele; Pei, Long; Ehrnstrom, Mats. (2017) Symmetry and decay of travelling wave solutions to the Whitham equation. Analysis and PDE Seminar, University of Lyon I ; 2017-03-21 - 2017-03-21.
-
Academic lectureEhrnstrom, Mats. (2017) Existence of a highest wave in a fully dispersive two-way shallow water model. Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory ; Athens, Georgia. 2017-03-28 - 2017-03-31.
-
Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive equations. PDE seminar, Lund University ; Lund. 2017-06-29 - 2017-06-29.
-
Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive nonlocal wave equations. Oberseminar in Analysis und Physik ; Leibniz Universität Hannover. 2017-01-17 - 2017-01-17.
-
Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full dispersion Kadomtsev–Petviashvili equation. Numerical Analysis and PDE seminar, L'université Paris-Sud (Paris-XI) ; Orsay, Paris. 2017-05-11 - 2017-05-11.
-
Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full dispersion Kadomtsev–Petviashvili equation. ICERM Semester Program on "Singularities and Waves In Incompressible Fluids": Workshop on Water Waves ; ICERM, Brown University, Providence. 2017-04-24 - 2017-04-28.
-
Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, Fields Institute ; Fields Institute, Toronto. 2017-08-08 - 2017-08-12.
-
Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Session on Nonlinear PDE, Catalan, Spanish, Swedish Math Meeting 2017 ; Umeå. 2017-06-13 - 2017-06-15.
-
Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2017) Two-Dimensional Bifurcation in the Whitham equation with surface tension. IMACS Conference ; Athens. 2017-03-30.
2016
-
Academic lectureEhrnstrom, Mats. (2016) A presentation of the mathematical theory for the highest wave of the Whitham equation in connection to the awarding of the Wallenberg prize 2016. Svenska Matematikersamfundets årsmöte ; 2016-06-17.
-
Academic lectureEhrnstrom, Mats. (2016) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberseminar Analysis und Physik ; Leibniz Universität Hannover. 2016-02-01.
-
Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Theoretical and Computational Aspects of Nonlinear Surface Waves . Banff International Research Station (BIRS); Banff. 2016-10-31 - 2017-12-04.
-
Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop ”Recent progress on the qualitative properties of nonlinear dispersive equations and systems” (Wolfgang Pauli Institute) ; 2016-09-19 - 2016-09-23.
-
Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop on Interactions between Partial Differential Equations and Functional Inequalities (Institut Mittag-Leffler) ; Stockholm. 2016-09-12 - 2016-09-16.
-
Academic lectureEhrnstrom, Mats. (2016) Symmetry and decay properties of traveling wave solutions to the Whitham equation. Differential Equations Seminar ; University of Missouri. 2016-12-03.
-
Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2016) Two-dimensional bifurcation in the Whitham Equation with surface tension. AIMS Conference ; 2016-07-05.
2015
-
Academic lectureEhrnstrom, Mats. (2015) Multi-dimensional bifurcation of steady water waves with vorticity. SIAM Conference on Analysis of Partial Differential Equations ; 2015-12-06 - 2016-12-10.
-
Academic lectureEhrnstrom, Mats. (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Online seminar on Applied Partial Differential Equations (University of Washington) ; 2015-10-15.
-
Popular scientific lectureEhrnstrom, Mats. (2015) Water Waves --- a mathematician's apology for dispersive equations. Matematiske perler, Institutt for matematiske fag ; 2015-10-16.
2014
-
InterviewLein, Hilde Lea; Brøseth, Heidi; Ehrnström, Mats Harald Andreas; Krokan, Arne; Mikkelsen, Solveig. (2014) Prosjekt Innovativ undervisning: Gjennombrudd for omvendt undervisning. universitetsavisa.no [Internett]. 2014-01-10.