Mats Ehrnstrom
Om
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. N. Arnesen, M. Ehrnstrom and A. G. Stefanov. A maximisation technique for solitary waves: the case of the nonlocally dispersive Whitham equation. 41 pages. arxiv:2303.14036
- 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
Publikasjoner
2023
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Vitenskapelig artikkel
-
Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2023)
On the precise cusped behaviour of extreme solutions to Whitham-type equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Vitenskapelig artikkel
2022
-
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
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A
Vitenskapelig artikkel
2020
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2020)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Vitenskapelig artikkel
2019
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Remonato, Filippo;
Mæhlen, Ola Isaac Høgåsen;
Johnson, Mathew A.
(2019)
On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation.
Water Waves
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
2018
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
-
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.)
Vitenskapelig artikkel
2017
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Vitenskapelig artikkel
-
Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
Vitenskapelig artikkel
2015
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics
Vitenskapelig artikkel
2014
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis
Vitenskapelig artikkel
2013
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Vitenskapelig artikkel
-
Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, Bogdan-Vasile.
(2013)
Steady-state fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Vitenskapelig artikkel
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
Vitenskapelig artikkel
2011
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Vitenskapelig artikkel
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Vitenskapelig artikkel
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
Tidsskriftspublikasjoner
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Vitenskapelig artikkel
-
Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2023)
On the precise cusped behaviour of extreme solutions to Whitham-type equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2020)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Remonato, Filippo;
Mæhlen, Ola Isaac Høgåsen;
Johnson, Mathew A.
(2019)
On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation.
Water Waves
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
-
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.)
Vitenskapelig artikkel
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Vitenskapelig artikkel
-
Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
Vitenskapelig artikkel
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports
Vitenskapelig artikkel
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics
Vitenskapelig artikkel
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis
Vitenskapelig artikkel
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Vitenskapelig artikkel
-
Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, Bogdan-Vasile.
(2013)
Steady-state fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Vitenskapelig artikkel
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Vitenskapelig artikkel
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Vitenskapelig artikkel
-
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
Vitenskapelig artikkel
Formidling
2022
-
Vitenskapelig foredragEhrnstrom, 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
-
Vitenskapelig foredragEhrnstrom, 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 -
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
2018
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, Mats. (2018) On waves of greatest height in fully dispersive nonlocal wave equations. PDE seminar , University of Warsaw 2018-03-22 - 2018-03-22
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Vitenskapelig foredragEhrnstrom, Mats. (2018) Travelling water waves with localised vorticity. NMF National meeting of mathematicians , Bergen 2018-09-14 - 2018-09-14
2017
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive equations. PDE seminar, Lund University , Lund 2017-06-29 - 2017-06-29
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Faglig foredragBruell, 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
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Faglig foredragBruell, 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
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Faglig foredragBruell, 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
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Vitenskapelig foredragRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2017) Two-Dimensional Bifurcation in the Whitham equation with surface tension. IMACS Conference , Athens 2017-03-30 -
-
Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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
2016
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Vitenskapelig foredragEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Banff International Research Station (BIRS) Theoretical and Computational Aspects of Nonlinear Surface Waves , Banff 2016-10-31 - 2017-12-04
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Vitenskapelig foredragRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2016) Two-dimensional bifurcation in the Whitham Equation with surface tension. AIMS Conference 2016-07-05 -
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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 -
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Vitenskapelig foredragEhrnstrom, Mats. (2016) Symmetry and decay properties of traveling wave solutions to the Whitham equation. Differential Equations Seminar , University of Missouri 2016-12-03 -
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Vitenskapelig foredragEhrnstrom, 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
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Vitenskapelig foredragEhrnstrom, 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 -
2015
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Vitenskapelig foredragEhrnstrom, 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 -
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Populærvitenskapelig foredragEhrnstrom, Mats. (2015) Water Waves --- a mathematician's apology for dispersive equations. Matematiske perler, Institutt for matematiske fag 2015-10-16 -
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Vitenskapelig foredragEhrnstrom, 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
2014
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IntervjuLein, Hilde Lea; Brøseth, Heidi; Ehrnström, Mats Harald Andreas; Krokan, Arne; Mikkelsen, Solveig. (2014) Prosjekt Innovativ undervisning: Gjennombrudd for omvendt undervisning. universitetsavisa.no universitetsavisa.no [Internett] 2014-01-10