Seminar on partial differential equations

On the well-posedness of an inviscid fluid-structure interaction model

Amjad Tuffaha

American University of Sharjah

Tuesday, 8. November 2022 - 9:00 to 10:00

in IM, rear building, ground floor and on Zoom:

Link: https://cesnet.zoom.us/j/96540133449?pwd=UVN4bHA5bEhCNVNZMXpQYlhkc3ZQZz09

Meeting ID: 965 4013 3449

Passcode: 285715

The recording of the lecture is available at: https://download.math.cas.cz/media/seminars/PDE/Necas_PDE_Seminar,_November_8,_2022_1.mp4

We consider the Euler equations on a domain with free moving interface. The motion of the interface is governed by a 4th order linear Euler-Bernoulli beam equation. The fluid structure interaction dynamics are realized through normal velocity matching of the fluid and the structure in addition to the aerodynamic forcing due to the fluid pressure.

We derive a-priori estimates and construct local-in-time solutions to the system in the Sobolev space H^r, with r>5/2. We also establish uniqueness in the Sobolev space H^r with r>3. An important consequence of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is joint work with Igor Kukavica.

We derive a-priori estimates and construct local-in-time solutions to the system in the Sobolev space H^r, with r>5/2. We also establish uniqueness in the Sobolev space H^r with r>3. An important consequence of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is joint work with Igor Kukavica.