Florian Kogelbauer, MSc BSc Some Topics in Mathematical Water

FAKULTAT
FUR
MATHEMATIK
Dekan Univ.{Prof. Dr. Harald Rindler
Einladung zur oentlichen Defensio von
Florian Kogelbauer, MSc BSc
Thema der Dissertation:
Some Topics in Mathematical Water Wave Theory
Abstract:
We will be concerned with the irrotational, nonlinear water wave problem in nite depth.
It consists of the inviscid Euler equations for an incompressible uid together with dynamic
and kinematic boundary conditions at the free surface.
The rst part of the talk is devoted to the study of the relation between traveling wave
solutions to this system and symmetry properties of the ow and the free surface. In
particular, we will prove that a solution to the governing equations with symmetric wave
prole as well as symmetric horizontal velocity at the free surface necessarily denes a
traveling wave. A similar result holds true for the acceleration and the horizontal velocity
component at the at bed.
In the second part, we will study a variational formulation of the water wave problem
and analyze its linear stability properties. We formulate stability conditions in terms of
physical quantities and Plotnikov's Potential. To this end, we use estimates for the Hilbert
transform on a strip and a coordinate transform in the innite part of the Lagrangian, as
well as spectral properties of matrices of operators.
Prufungssenat:
Univ.-Prof. Dr. Josef Hofbauer (Vorsitz)
(Universitat Wien)
Univ.-Prof. Dr. Adrian Constantin
(Universitat Wien)
Univ.-Prof. Dr. Gerald Teschl
(Universitat Wien)
Prof. Dr. Jean-Marc Vanden-Broeck
(University College London)
Privatdoz. PhD Calin-Iulian Martin
(Universitat Wien)
Zeit:
Ort:
Mittwoch, 16. Marz 2016, 14:30 Uhr
Fakultat fur Mathematik, Besprechungsraum 09. Stock, Oskar-Morgenstern-Platz 1

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