Okay.

Now I'm recording so...

Okay, so do you see it?

Yeah.

Do you see it correctly?

I see it correctly.

Maybe the audience also should be seeing it correctly.

Okay.

So if I see you see it in full screen?

Right.

Okay.

So I can begin in this case.

Okay.

Yeah, you can start.

Okay.

So thanks for the invitation.

I must confess I'm not at all accustomed to this Zoom stuff.

So I I bothered a lot Marius with a lot of questions before and okay hopefully it will

work.

So the the object of my talk is the long-time behavior in a class of free structure interactions

problems.

So please I don't know if you how easy is to interrupt or not with this system so but

if it's reasonable please do it and especially if you don't see or hear good enough.

So now let me say the let's say a very graphic description of the type of problems I'm interested

in.

So you have a body in my case it will always be rigid which is in a fluid and then you

just give an let's say a kind of initial velocity to the body eventually to the fluid around

and you wait and see what will what will the solid do.

So what we we are interested in is what is the behavior of a solid when t goes to infinity.

Let me go to three examples.

So at the left you have a very simplified representation of a rigid body in a viscous

fluid which here it will be in 2D in the picture but it can be in 3D in my results it will

be in 3D and then this can be the fluid can be inside a container as in the picture but

it can also assuming that it's something like a lake or an ocean you can assume it infinite

because you can say that the exterior boundary plays no role.

So in this case a legitimate question is mathematically speaking what happens if you give an initial

impulse to the body and then wait.

So a philosophical question could be will it stop somewhere or will it go to infinity

if my fluid is an infinite domain.

A different situation is in the middle this is a piston.

So here the solid it's more complicated but forgetting about this mechanism which you

have just the cylinder here the small cylinder here which is a piston and you have a round

of the fluid will be a guess a compressible fluid and the same question can occur you

here you are for necessarily in a boundary domain in my picture you give an impulse to

the piston what happens when t goes to infinity.

A slightly different situation is at the right where the body is floating this is a very

simplified representation of something called a point absorber for wave energy converter.

So the idea is that where I have this flash you can have instead have a mechanism and

you which keeps the body vertical so it can go up and down with the waves in the ocean

and when it goes up and down this mechanism is let's say absorbing energy absorbing the