35:37
publiée le 8 avril 2024
On the Radon-Carleman problem in uniformly rectifiable domains
De Irina Mitrea
Multiple traveling waves of the Euler-Korteweg system
Apparaît dans la collection : Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution / Fluides inhomogènes : modèles asymptotiques et évolution d'interfaces
The Euler-Korteweg system corresponds to compressible, inviscid fluids with capillary forces. It can be used to model diffuse interfaces. Mathematically it reads as the Euler equations with a third order dispersive perturbation corresponding to the capillary tensor.
In dimension one there exists traveling waves with equal or different limit at infinity, respectively solitons and kinks. Their stability is ruled by a simple criterion a la Grillakis-Shatah-Strauss. This talk is devoted to the construction of multiple traveling waves, namely global solutions that converge as $t\rightarrow \infty $ to a profile made of several (stable) traveling waves. The waves constructed have both solitons and kinks. Multiple traveling waves play a peculiar role in the dynamics of dispersive equations, as they correspond to solutions that follow in some sense a purely nonlinear evolution.
