Short··0:12·Partial differential equations
Relativistic Vlasov-Maxwell: Global Solutions
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About this video
Global classical solutions of the three-dimensional relativistic Vlasov-Maxwell system
Can a collisionless relativistic plasma stay smooth? OpenAI's manuscript reports global existence and uniqueness of classical solutions to the three-dimensional one-species relativistic Vlasov-Maxwell system. It assumes smooth nonnegative compactly supported particle data and smooth finite-energy electromagnetic fields with bounded derivatives and compatible divergence constraints. No smallness or symmetry assumption is imposed. The compact-support bound is on each finite time interval; it may grow with that interval.
Paper: Global classical solutions of the three-dimensional relativistic Vlasov-Maxwell system
github.com/openai/math/blob/main/preprints/Global-classical-s…
About the animation: Analytic closed helical trajectories and field curves illustrate charged transport in a schematic magnetic bottle. A dominant particle leaves a tapered wake that grows into a full closed path; fainter companion paths appear during the wide reveal. The camera follows the particle, and turnaround highlights at 2.9333 and 8.45 seconds align with measured soundtrack accents. The trajectories are editorial geometry, not a self-consistent numerical solution of the coupled Vlasov-Maxwell PDE or evidence for particle confinement. Electric blue distinguishes the field scaffold; amber and ivory distinguish particle paths. Colours do not encode charge sign, speed, temperature or field strength. Playback timing is editorially warped. The actual transport equation remains displayed.
GitHub repository: github.com/openai/math
Related formalization scope: github.com/openai/math/blob/main/lean/docs/362.md
The linked scope documents the stated classical-solution result. The formalization was not executed or audited in this production.
Source-reported result. Selected theorem statements and scope were read; this is not an independent proof audit.
'Aurora' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
scottbuckley.com.au/library/aurora/
Licence: creativecommons.org/licenses/by/4.0/
Music edits: excerpted, crossfaded for looping, and gain adjusted.
About the problem
Partial differential equations·OpenAI Math·Result 362
Global smoothness for relativistic Vlasov–Maxwell
Proves large-data global existence and uniqueness for the three-dimensional, one-species relativistic Vlasov–Maxwell system. Smooth admissible initial data may be arbitrary provided the particle density is compactly supported and the electromagnetic fields have finite energy and bounded derivatives of every order; the solution remains smooth on every finite time interval. (Lean)
Topics
Vlasov-Maxwellrelativistic Vlasov-Maxwellglobal classical solutionsplasma physicskinetic theoryLorentz forcepartial differential equationsOpenAI math3D math animation
