Analysis and Probability seminar

​​Jörg Weber, Lund: Travelling periodic water waves
While the research on water waves modelled by Euler's equations has a long history, mainly in the last two decades travelling periodic rotational waves have been constructed with mathematical rigour by means of bifurcation theorems. After introducing the problem, I will present a new reformulation of this travelling periodic water wave problem in two dimensions. Using conformal mappings and a new reformulation of Bernoulli's equation, the problem is equivalently cast into the form “identity plus compact”, which is amenable for Rabinowitz' global bifurcation theorem. The main advantages (and the novelty) of this new reformulation are that no simplifying restrictions on the geometry of the surface profile and no simplifying assumptions on the vorticity distribution (and thus no assumptions regarding the absence of stagnation points or critical layers) have to be made. Within the scope of this new formulation, local and global families of solutions, bifurcating from laminar flows with a flat surface, are constructed. Moreover, I will further discuss the condition for local bifurcation and the possible alternatives for the global set of solutions, as well as their nodal properties. This is joint work with Erik Wahlén.
​Should you have any questions or suggestions, feel free to email one of the organizers Jakob Björnberg (jakobbj 'at', Probability Theory), Erik Broman (broman 'at', Probability Theory) or Clemens Weiske (weiske 'at', Analysis).
Category Seminar
Location: MV:L14 and zoom
Starts: 27 September, 2022, 13:15
Ends: 27 September, 2022, 14:15

Page manager Published: Tue 20 Sep 2022.