(page edited on the 03/04/22)

First year PhD student of David Lannes at the IMB in Bordeaux, France.

Thesis title : Boundary problems in surface hydrodynamics

Theses description :

Wave propagation at the surface of a fluid is fairly well understood when considering that the volume occupied by the fluid does not have
lateral bounds. The free surface Euler equations are then wellposed, aswell as most asymptotic models used by oceanographers for numerical
simulations in coastal oceanography (Saint-Venant, Boussinesq or Green-Naghdi equations, among many others...). However, much less is known when there is a lateral bound, whether fictive (as in mixed problems or transparent boundary conditions), or physical (a rising bottom topography as in a beach shore, an interaction with a bridge pile or a floatting object). To this day, this kind of problems is only well-understood in the hyperbolic case (that is for the Saint-Venant equations) and in space dimension equals to one. The other cases being open, and my research concerns these aspects of fluid dynamics. There are two main obstacles : the understanding of the singularities at the boundary in dimension two, and the role of the dispersion. Bridging this gap could reveal useful in coastal oceanography.

Contact : matthieu.pauron@math.u-bordeaux.fr