Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Speaker: Ovidiu-Neculai Avadanei (University of Wisconsin, Madison and University of California, Berkeley)

Title: Well-posedness for the dispersive Hunter-Saxton equation

Abstract: This talk represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals, and is known to be completely integrable. Although the equation has formal similarities with the KdV equation, the lack of $L^2$ control gives it a quasilinear character, with only continuous dependence on initial data.

Here, we prove the local and global well-posedness of the Cauchy problem using a normal form approach to construct modified energies, and frequency envelopes in order to prove the continuous dependence with respect to the initial data. (Joint work with Albert Ai).

Speaker: Mathieu Pauron (Université de Bordeaux)

Title: The dead water phenomenon, an example of fluid-structure problem



Abstract : The study of fluid-structure interaction is a domain of fluid mechanics which amounts to understanding the evolution of a system coupling a fluid and a solid, the basic example being the study of a boat floating on the sea. The dead water phenomenon is another example of a fluid-structure interaction problem. A boat floats on two layers of water, each with a fixed density. When the boat starts moving, a wave builds up at the interface and slows the boat, up until it stops. The goal of the talk is to present the framework of the study of this problem and the tools developed by Lannes, Iguchi and others to deal with the hyperbolic approximation of this system.

Well-Posedness for the Dispersive Hunter-Saxton Equation

The Dead Water Phenomenon, an Example of Fluid-Structure Problem