Okay, welcome everyone.

Welcome everyone.

So today we have Dr. Joerg Weber,

who just moved to Sweden from the University of Vero

to the Lund University in Sweden,

where he's having a post-op position.

And he will be speaking today about the relativistic class

of Maxwell system with external electromagnetic fields.

This year, you have the floor.

Yeah, so thank you very much for the invitation

and the opportunity to speak in your seminar.

So yes, this is basically my PhD thesis

I want to talk about today.

So back in Vero, I did this PhD thesis, as you said.

And so what's the motivation of the problem I considered?

And we will consider the following.

So if you consider, for example, a fusion reactor.

So for example, here you can see a Tockelmann reactor,

where you have a chamber, for example, typically

a total shape chamber, where inside this chamber

there is plasma.

So there the fusion happens somehow.

And in the outside, there are electric coils,

as you can see in the outside.

And they generate external electromagnetic fields

that somehow want to influence or control

the internal plasma so that the plasma somehow stays

in a certain shape or so that the fusion may work.

And so that plasma is also confined

so that the reactor chamber, the wall,

is not damaged by plasma particles hitting it.

So that's the setting.

So that's the motivation somehow.

We have a plasma in a container, so typically a torus.

But this doesn't have to be a torus at all in our analysis.

You denote this container by omega.

And outside, we have some external currents

that may later serve as a control, for example.

And then one can ask some questions.

So what are differential equations that somehow model

this situation?

So there are different approaches

on different differential equations

that can model this.

For example, also a common model is fluid dynamics.

So a fluid model, magneto-hydrodynamics,

MHT, or the plasma model by a fluid model, as I said.

This is also often used, has the afford

that you only have three dimensional phase space.

So we'll come to this point later.