PDE and Fluid Mechanics

The study of the partial differential equations arising from Fluid Mechanics is of great importance both from the applied and theoretical point of view. For example the relevance of the understanding of the Navier-Stokes equations (incompressible fluids) has been highlighted by the choice of the global existence of solutions as one of the Millenium Problems by the Clay Institute for which one million dollars has been offered.The proposed activities revolve around the organization of a workshop involving the international leading researchers in PDE and Fluid Mechanics., to expose the UK to the new developments in the area. We expect to create a platform for the interaction of all participants, to promote the development of new research links and collaborations. This includes the involvement of graduate students and post-docs with poster sessions.In addition, and linked to their participation in the workshop some speakers will spend extended visits (up to 2 extra weeks) to continue collaboration with the PI on the evolution of sharp fronts for surface quasi-geostrophic equation and its connections with the Euler equation (Charles Fefferman) and the co-PI on partial regularity for Navier Stokes (Igor Kukavica). Additional, similar arrangements might be made with some other speakers.

The main beneficiaries of the proposed activities will be researchers in the area of Fluid Mechanics and PDE. The workshop in itself provides and excellent opportunity for the interaction of UK researchers with the leading international experts, while exposing the UK community to the recent developments in the area. Funds are being requested to partially support 10 graduate students and post-docs. The workshop will provide an opportunity for the dissemination of their work (via poster sessions) and for the creation of new links to develop their future research career. We are expecting the publication of a volume of proceedings that will allow for the dissemination of research and to engage the community at large. Both the PI and co-PI have great experience in the organization of workshop and in the editing of proceedings (for example following a conference at Warwick in May 2007 we jointly edited the volume Partial Differential Equations and Fluid Mechanics . London Mathematical Society Lecture Note Series (No. 364), Cambridge University Press. Eds. J.C. Robinson & Jose L. Rodrigo (2009)) In addition the work resulting from the collaborations during the extended visits of some of the speakers will be disseminated via publications in internationally recognized peer-reviewed journals and through lectures in conferences and seminars.