Partial Differential Equations

On the collapse mechanism of Wave Maps

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B1 L4 R4214

The Wave Map system describes the evolution of waves constrained on a (Riemannian) manifold. For the 2 + 1 dimensional problem, when the target manifold is a sphere, the solution collapses in finite time. The Analysis is due to the pioneering work of Merle, Paphael and Rodnianski. Motivated by their work I will present a somewhat novel approach of the collapsing mechanism which is based on a view of the equations as a nonlinear gauge system. This is joint work with Dan Geba.

Meet KAUST prospective student: Stefanos Georgiadis

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Stefanos Georgiadis is an applied mathematics graduate who will join KAUST from the School of Applied Mathematical and Physical Sciences, Athens, Greece. Stefanos will join KAUST this fall as a Ph.D. candidate and member of the Applied Partial Differential Equations (AppliedPDE) research group under the supervision of Professor Athanasios Tzavaras.

Stefanos Georgiadis

Stefanos Georgiadis is a Ph.D. candidate in a co-tutelle between KAUST and TU Wien, under the supervision of Professor Athanasios Tzavaras and Ansgar Jüngel. Before joining KAUST, Stefanos obtained his bachelor and master's degree in applied mathematics from the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens in Greece. Research Interests Stefanos' research interests include the analysis of nonlinear partial differential equations as they apply to the modeling of multicomponent systems of gases.

Nuno J. Alves

Short Bio Mr. Nuno Alves is a Ph.D student in the AppliedPDE group of the Applied Mathematics and Computational Science program (AMCS) of CEMSE division at the King Abdullah University of Science and Technology, Saudi Arabia. He has got bachelor and master's degrees from Instituto Superior Tecnico, University of Lisbon, Portugal. Mr. Nuno had been a visiting student at KAUST from March 2014 to July 2014. Moreover, during the academic year 2017/2018 he was working as an invited teaching assistant at Polytechnic Institute of Beja, Portugal. His work is essentially related with non-linear partial

Athanasios Tzavaras

KAUST Professor of Applied Mathematics and Computational Science Athanasios (Thanos) Tzavaras specializes in mathematical modelling, analysis and computation of partial differential equations pertaining to fluid mechanics or modeling of materials.