#### Speaker:

### Dr. Lê Đức Hưng

#### Title:

## On the existence and instability of solitary water waves with a finite dipole

#### Time:

16:00 Thursday December 23, 2021 (VN time)

#### Place:

online at https://meet.google.com/fkz-fbuf-cvz

#### Abstract:

This talk considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is air and that the waves are acted upon by gravity with surface tension effects on the air-water interface. In particular, we study the case where there is a finite dipole in the bulk of the fluid, that is, the vorticity is a sum of two weighted delta-functions. Using an implicit function theorem argument, we construct a family of solitary waves solutions for this system that is exhaustive in a neighborhood of 0. Our main result is that this family is conditionally orbitally unstable. This is proved using a modification of the Grillakis–Shatah–Strauss method recently introduced by Varholm, Wahlén, and Walsh.

#### Brief biography:

Lê Đức Hưng received his BSc from the University of Washington, his PhD from the University of Missouri at Columbia in 2019, and worked as a postdoc at Norwegian University of Science and Technology. His research area is partial differential equations, in particular those arising from fluid and water waves.

Speaker: Dr. Phan Thị Mỹ Duyên (Gran Sasso Science Institute, Italy)

Title:

## Numerical validation of homogeneous multi-fluid models

Time: 14:00 Wednesday November 3, 2021 (VN time)

Place: online at: https://meet.google.com/fkz-fbuf-cvz

Abstract:

Wave propagation in heterogeneous mixtures is an important subject of continuum mechanics appearing in many physical and industrial situations: shock waves in fluids containing gas bubbles, sound wave propagation in layered systems such as composite materials or earth’s layers (crust, upper mantle, lower mantle), modeling loss of coolant accident in nuclear reactor systems, and so on. In this seminar, I will talk about a multi-fluid problem that we consider a 1D periodic system containing a large number of layers. Each layer is composed of two sub-layers of compressible fluids having different densities and equations of state. I will present a comparison between a detailed numerical solution of the Euler equations that govern the multi-layer system, and two isentropic homogeneous (average) models effectively describing such a complex two-fluid mixture.