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. Fields of science natural sciencesphysical sciencesclassical mechanicsfluid mechanicsfluid dynamicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsmathematical model Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-StG-2015 - ERC Starting Grant Call for proposal ERC-2015-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution LUNDS UNIVERSITET Net EU contribution € 1 203 627,00 Address Paradisgatan 5c 22100 Lund Sweden See on map Region Södra Sverige Sydsverige Skåne län Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 203 627,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all LUNDS UNIVERSITET Sweden Net EU contribution € 1 203 627,00 Address Paradisgatan 5c 22100 Lund See on map Region Södra Sverige Sydsverige Skåne län Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 203 627,00
