| Abstract: |
| We consider the three-dimensional relativistic Vlasov-Maxwell-Boltzmann system, where the speed of light $c$ is
an arbitrary constant no less than 1, and we establish global existence and nonlinear stability of the vacuum for small
initial data, with bounds that are uniform in $c$. The analysis is based on the vector field method combined with the
Glassey-Strauss decomposition of the electromagnetic field, and does not require any compact support assumption
on the initial data. A key ingredient of the proof is the derivation of a chain rule for the relativistic Boltzmann collision
operator that is compatible with the commutation properties of the vector fields. These tools allow us to control the
coupled kinetic and electromagnetic equations and to obtain global stability near vacuum. This is a joint work with Chuqi Cao. |
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