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 blowup
 Datadriven 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 Largescale interdisciplinary researcher project IMod. Partial differential equations, statistics and data: An interdisciplinary approach to databased 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 Whithamtype equations. 30 pages. arxiv:2302.08856
Publications
2024

Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2024)
On the precise cusped behaviour of extreme solutions to Whithamtype equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article
2023

Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Academic article
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
Academic article

Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
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
Academic article
2019

Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
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
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
Academic article
2018

Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Smallamplitude fully localised solitary waves for the fulldispersion KadomtsevPetviashvili equation.
Nonlinearity
Academic article

Ehrnstrom, Mats;
Johnson, Mathew A;
Claassen, Kyle M.
(2018)
Existence of a Highest Wave in a Fully Dispersive TwoWay Shallow Water Model.
Archive for Rational Mechanics and Analysis
Academic article

Ehrnstrom, Mats;
Pei, Long.
(2018)
Classical wellposedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces.
Journal of evolution equations (Printed ed.)
Academic article
2017

Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Academic article

Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
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 wellposedness for the whitham equation.
Springer Proceedings in Mathematics
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;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Academic article

Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, BogdanVasile.
(2013)
Steadystate fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Academic article
2012

Ehrnström, Mats Harald Andreas;
Groves, Mark;
Wahlén, E..
(2012)
On the existence and stability of solitarywave solutions to a class of evolution equations of Whitham type.
Nonlinearity
Academic article
2011

Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Academic article

Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Academic article

Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Academic article

Ehrnström, Mats;
Escher, J.;
Matioc, B.V..
(2011)
Wellposedness, instabilities, and bifurcation results for the flow in a rotating HeleShaw cell.
Journal of Mathematical Fluid Mechanics
Academic article
Journal publications

Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2024)
On the precise cusped behaviour of extreme solutions to Whithamtype equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article

Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
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
Academic article

Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
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
Academic article

Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
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
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
Academic article

Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Smallamplitude fully localised solitary waves for the fulldispersion KadomtsevPetviashvili equation.
Nonlinearity
Academic article

Ehrnstrom, Mats;
Johnson, Mathew A;
Claassen, Kyle M.
(2018)
Existence of a Highest Wave in a Fully Dispersive TwoWay Shallow Water Model.
Archive for Rational Mechanics and Analysis
Academic article

Ehrnstrom, Mats;
Pei, Long.
(2018)
Classical wellposedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces.
Journal of evolution equations (Printed ed.)
Academic article

Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Academic article

Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
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 wellposedness for the whitham equation.
Springer Proceedings in Mathematics
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;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Academic article

Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, BogdanVasile.
(2013)
Steadystate fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Academic article

Ehrnström, Mats Harald Andreas;
Groves, Mark;
Wahlén, E..
(2012)
On the existence and stability of solitarywave solutions to a class of evolution equations of Whitham type.
Nonlinearity
Academic article

Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Academic article

Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Academic article

Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Academic article

Ehrnström, Mats;
Escher, J.;
Matioc, B.V..
(2011)
Wellposedness, instabilities, and bifurcation results for the flow in a rotating HeleShaw cell.
Journal of Mathematical Fluid Mechanics
Academic article
Knowledge Transfer
2023

Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Seminar of Analysis, EPFL , École polytechnique fédérale de Lausanne 20230317 

Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Aspects of Nonlinear Evolution. Conference in Honor of the 60th Birthday of Joachim Escher , Leibniz Universität Hannover 20230531  20230602

Popular scientific lectureEhrnstrom, Mats. (2023) On Euler’s musical function and other topics in the mathematical theory of music. Mathematical Pearls , NTNU 20231020 

Academic lectureEhrnstrom, Mats. (2023) Equations with very low order of dispersion. An overview and description of new results. Order and Randomness in Partial Differential Equations Water Waves and Integrable Systems. Workshop at Institut MittagLeffler. Dedicated to the memory of Thomas Kappeler , Institut Mittag–Leffler, Stockholm 20230911  20230915

Popular scientific lectureEhrnstrom, Mats. (2023) Topdown and bottomup: how the measureprone can meet the principledriven. IE Friday Talk , NTNU 20230929 

Academic lectureEhrnstrom, Mats. (2023) Mathematics in Water Waves. Colloquium at Linköping University , Linköping University 20230906 

Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Workshop on Nonlinear Waves and Related Topics, Kanagawa , Shonan Village Center 20231106  20231110
2022

Academic lectureEhrnstrom, Mats. (2022) Smooth stationary water waves with exponentially localised vorticity. Program on Geometric Aspects of Nonlinear Partial Differential Equations , Institut MittagLeffler, Stockholm 20221115 

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 20220930  20221001

Academic lectureEhrnstrom, Mats. (2022) Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvili equation. 2nd Norwegian meeting on PDEs , Bergen 20220608  20220610

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, Dijon , University of Burgundy 20220613  20220617
2021

Academic lectureEhrnstrom, Mats. (2021) On the bifurcation diagram of the capillarygravity Whitham equation. Online Seminar on Nonlinear Water Waves and Related Topics , Ibaraki University 20211119 

Academic lectureEhrnstrom, Mats. (2021) Constructions and properties of mathematical solutions to water wave equations. Hausdorff Colloquium , University of Bonn 20210609 

Popular scientific lectureEhrnstrom, Mats. (2021) The HardyWeinberg Principle and Evolutionary Genetics. Mathematical Pearls , NTNU 20211203 

Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. Mathematics of Fluid Dynamics program , MSRI, Berkeley 20210406 

Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. PDE seminar, University of Missouri , University of Missouri (online) 20210415 

Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. PDE seminar, Lanzhou , Lanzhou University 20210528 
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 20180708  20180708

Academic lectureEhrnstrom, Mats. (2018) Enhanced existence time of solutions to the fractional Korteweg—de Vries equation. Oneday seminar on Geometry, Analysis and PDEs , Bergen 20181022  20181022

Academic lectureEhrnstrom, Mats. (2018) On waves of greatest height in fully dispersive nonlocal wave equations. PDE seminar , University of Warsaw 20180322  20180322

Academic lectureEhrnstrom, Mats. (2018) Travelling water waves with localised vorticity. NMF National meeting of mathematicians , Bergen 20180914  20180914
2017

Academic lectureEhrnstrom, Mats. (2017) Smallamplitude solitary waves for the fulldispersion KadomtsevPetviashvili equation. Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, Fields Institute , Fields Institute, Toronto 20170808  20170812

Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive equations. PDE seminar, Lund University , Lund 20170629  20170629

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 20170321  20170321

LectureBruell, Gabriele; Pei, Long; Ehrnstrom, Mats. (2017) On symmetry and decay of travelling wave solutions to a nonlocal dispersive equation. Analysis Seminar, TU Delft 20170504  20170504

LectureBruell, Gabriele; Ehrnstrom, Mats; Pei, Long. (2017) On symmetry and decay of travelling solutions to a nonlocal dispersive equation. Nonlinear Evolution Equations/Wave Phenomena 20170328  20170331

Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2017) TwoDimensional Bifurcation in the Whitham equation with surface tension. IMACS Conference , Athens 20170330 

Academic lectureEhrnstrom, Mats. (2017) Smallamplitude solitary waves for the full dispersion Kadomtsev–Petviashvili equation. Numerical Analysis and PDE seminar, L'université ParisSud (ParisXI) , Orsay, Paris 20170511  20170511

Academic lectureEhrnstrom, Mats. (2017) Smallamplitude solitary waves for the fulldispersion KadomtsevPetviashvili equation. Session on Nonlinear PDE, Catalan, Spanish, Swedish Math Meeting 2017 , Umeå 20170613  20170615

Academic lectureEhrnstrom, Mats. (2017) Smallamplitude 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 20170424  20170428

Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive nonlocal wave equations. Oberseminar in Analysis und Physik , Leibniz Universität Hannover 20170117  20170117

Academic lectureEhrnstrom, Mats. (2017) Existence of a highest wave in a fully dispersive twoway shallow water model. Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory , Athens, Georgia 20170328  20170331
2016

Academic lectureEhrnstrom, 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 20161031  20171204

Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2016) Twodimensional bifurcation in the Whitham Equation with surface tension. AIMS Conference 20160705 

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) 20160919  20160923

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 20160617 

Academic lectureEhrnstrom, Mats. (2016) Symmetry and decay properties of traveling wave solutions to the Whitham equation. Differential Equations Seminar , University of Missouri 20161203 

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 MittagLeffler) , Stockholm 20160912  20160916

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 20160201 
2015

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) 20151015 

Popular scientific lectureEhrnstrom, Mats. (2015) Water Waves  a mathematician's apology for dispersive equations. Matematiske perler, Institutt for matematiske fag 20151016 

Academic lectureEhrnstrom, Mats. (2015) Multidimensional bifurcation of steady water waves with vorticity. SIAM Conference on Analysis of Partial Differential Equations 20151206  20161210
2014

InterviewLein, Hilde Lea; Brøseth, Heidi; Ehrnström, Mats Harald Andreas; Krokan, Arne; Mikkelsen, Solveig. (2014) Prosjekt Innovativ undervisning: Gjennombrudd for omvendt undervisning. universitetsavisa.no universitetsavisa.no [Internet] 20140110