VORTSHEET · Vortex sheets - from new intuitions to crucial questions.
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2017-01-01 → 2018-12-31
- EU contribution
- €195,455
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Vortex sheets - from new intuitions to crucial questions.
The project contains a series of problems in Partial Differential Equations arising from Fluid Mechanics. Given the wide applicability of Fluid Mechanics in the Physical Sciences and Engineering it becomes therefore very relevant to understand fundamental properties of the equations that model the corresponding system. In the project we focus in equations in vortex dynamics, where the vorticity is the curl of velocity. We also focus on the Camassa-Holm equation. For these systems we consider the following issues: - Existence of solutions: Once a model has been posed, and described precisely by an partial differential equation, a fundamental question becomes understanding whether or not solutions actually exist, a result that might depend on the type of initial data prescribed. - Uniqueness of solutions: ideally once a system has been posed it is higly desirable to have only solution for each initial condition. Mathematically this is know as uniqueness of solutions. A key result of this project is the uniqueness of solutions for the Camassa-Holm equation. - Regulatiy of solutions: finally, once we have established the existence (and uniqueness) of a solution we want to understand mode qualitative properties of the solution, for example its regularity, and whether or not any singularities form. All of these issues are very relevant in mathematical context, but also crutially important to validate the model and test its accurate as a predictor of the behaviour of solutions in real-worl problems.
Data: CORDIS, © European Union
Project objective
Understanding fundamental phenomena in fluid mechanics, such as formation of vortices at wingtips of a plane taking off or development of repetitive turbulent patterns of clouds, requires studying special flows which are characterized by a jump of velocity across certain interfaces. These singular flows correspond to solutions of the classical Euler equations from inviscid fluid dynamics, called vortex sheets. Remarkably, the existence and uniqueness of vortex sheets remain outstanding open problems even though they are of vital importance in applications in aerodynamics and climatology.We aim to approach these problems from a new point of view and thus contribute to the development of the area. To achieve our goals we will- construct a new family of vortex sheets called 'vortex cusps',- study singularities, which vortex cusps may develop,- study related models to gain further intuitions.The project will be conducted at the University of Warwick under the supervision of a leading researcher in the field, J.L. Rodrigo. It will also include a secondment in Seville, hosted by F. Gancedo and short visits to other experts in the field (D. Cordoba, Ch. Fefferman, T.Cieslak). This setup guarantees the highest quality of academic training, which will significantly broaden the previous interdisciplinary expertise of G. Jamroz (who finished his PhD in Warsaw in January 2015 and is currently a postdoc in Basel) and will, in combination with an intensive transferable skills training, lead him to an independent researcher position. What is more, the project will strengthen the position of the University of Warwick as a top mathematical research centre by extending its network of collaborations across Europe. The results of the research will be actively and frequently communicated both to experts and general public by open-access and peer-reviewed publications as well as conferences and general public events, thus ensuring maximum outreach of the proposed action.
Original text from CORDIS.
Participants
- UNIVERSITY OF WARWICK · COVENTRYCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union