Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain · arXivDesk
2401.00554Dec 31, 2023Major revisions include the addition of a global well-posedness result. Further improvements are as follows: enhanced control of instant energies, more precise decay estimates of instant energies, and a significantly improved presentation. The manuscript now comprises 99 pages
Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain
The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classical perfect conducting conditions at the wall, E×nx=0,B⋅nx=0,
Nearby in the stack
plays an important role in fusion plasma dynamics studies. Since the early 1990s, it has been understood that the Lorentz force can penetrate into the domain at the boundary and create a singularity. Consequently, the uniqueness for any nonlinear kinetic plasma models in the presence of a perfectly conducting boundary remained open until our recent local well-posedness result. In this paper, we finally establish a global well-posedness theory for the relativistic Vlasov-Maxwell-Landau system in a general
3D
domain with a specularly reflective, perfectly conducting boundary.