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Global smoothness for relativistic Vlasov–Maxwell
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Difficulty:🧠🧠🧠🧠🧠 Ages:13 - ∞
Skills:fluids, heat, waves Levels:1
Category:Partial differential equations Lean version:YES! ✔
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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.

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released 2026-09-23  |  1 theorem · 16 lemmas · 21 proofs · 19,385 words  |  PLAY LEVEL 1 »  (pdf)
We prove global existence and uniqueness for arbitrary smooth admissible initial data in the three-dimensional, one-species relativistic Vlasov–Maxwell system. The particle density is initially compactly supported, and the electromagnetic fields have finite energy and bounded derivatives of all orders. The solution remains smooth on every finite time interval. This resolves the large-data global classical regularity problem for this model, without size or symmetry restrictions on the data.

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