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Mathematical aspects of three-dimensional water waves with vorticity

Total Cost €


EC-Contrib. €






Project "3DWATERWAVES" data sheet

The following table provides information about the project.


Organization address
address: Paradisgatan 5c
city: LUND
postcode: 22100
website: n.a.

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Sweden [SE]
 Project website
 Total cost 1˙203˙627 €
 EC max contribution 1˙203˙627 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-03-01   to  2021-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    LUNDS UNIVERSITET SE (LUND) coordinator 1˙203˙627.00


 Project objective

The goal of this project is to develop a mathematical theory for steady three-dimensional water waves with vorticity. The mathematical model consists of the incompressible Euler equations with a free surface, and vorticity is important for modelling the interaction of surface waves with non-uniform currents. In the two-dimensional case, there has been a lot of progress on water waves with vorticity in the last decade. This progress has mainly been based on the stream function formulation, in which the problem is reformulated as a nonlinear elliptic free boundary problem. An analogue of this formulation is not available in three dimensions, and the theory has therefore so far been restricted to irrotational flow. In this project we seek to go beyond this restriction using two different approaches. In the first approach we will adapt methods which have been used to construct three-dimensional ideal flows with vorticity in domains with a fixed boundary to the free boundary context (for example Beltrami flows). In the second approach we will develop methods which are new even in the case of a fixed boundary, by performing a detailed study of the structure of the equations close to a given shear flow using ideas from infinite-dimensional bifurcation theory. This involves handling infinitely many resonances.


year authors and title journal last update
List of publications.
2019 E. Lokharu, E. Wahlén
A variational principle for three-dimensional water waves over Beltrami flows
published pages: 193-209, ISSN: 0362-546X, DOI: 10.1016/
Nonlinear Analysis 184 2019-05-15
2019 Boris Buffoni, Erik Wahlén
Steady three-dimensional rotational flows : anapproach via two stream functions and Nash–Moser iteration
published pages: 1225-1258, ISSN: 2157-5045, DOI: 10.2140/apde.2019.12.1225
Analysis & PDE 12/5 2019-04-02

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