From the Vlasov–Maxwell–Boltzmann System to Incompressible Viscous Electro-magneto-hydrodynamics
Volume I
Diogo Arsénio
Université Paris Diderot, FranceLaure Saint-Raymond
École Normale Supérieure, Lyon, France
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| FrontmatterDownload pp. i–iv | |
| PrefaceDownload pp. v–viii | |
| ContentsDownload pp. ix–xii | |
| Part I Formal derivations and macroscopic weak stabilityp. 1 | |
| 1 | The Vlasov–Maxwell–Boltzmann systempp. 3–14 |
| 2 | Scalings and formal limitspp. 15–72 |
| 3 | Weak stability of the limiting macroscopic systemspp. 73–117 |
| Part II Conditional convergence resultsp. 119 | |
| 4 | Two typical regimespp. 121–156 |
| 5 | Weak compactness and relaxation estimatespp. 157–181 |
| 6 | Lower-order linear constraint equations and energy inequalitiespp. 183–198 |
| 7 | Strong compactness and hypoellipticitypp. 199–231 |
| 8 | Higher-order and nonlinear constraint equationspp. 233–262 |
| 9 | Approximate macroscopic equationspp. 263–311 |
| 10 | Acoustic and electromagnetic wavespp. 313–322 |
| 11 | Grad’s moment methodpp. 323–329 |
| 12 | The renormalized relative entropy methodpp. 331–382 |
| Appendicesp. 383 | |
| A | Cross-section for momentum and energy transferpp. 385–387 |
| B | Young inequalititespp. 389–392 |
| C | End of proof of Lemma 7.7 on hypoelliptic transfer of compactnesspp. 393–397 |
| Bibliographypp. 399–402 | |
| Indexpp. 403–406 |