Remark on the null-condition for the nonlinear wave equation
Tzvetkov, Nickolay
Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000), p. 135-145 / Harvested from Biblioteca Digitale Italiana di Matematica

Dimostriamo l'esistenza della soluzione globale per un sistema di equazioni delle onde con nonlinearità quadratica dipendente dalle variabili spazio-tempo. Come in [3] la tecnica è basata sulla trasformazione di Penrose.

Publié le : 2000-02-01
@article{BUMI_2000_8_3B_1_135_0,
     author = {Nickolay Tzvetkov},
     title = {Remark on the null-condition for the nonlinear wave equation},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3-A},
     year = {2000},
     pages = {135-145},
     zbl = {0949.35090},
     mrnumber = {1755705},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_1_135_0}
}
Tzvetkov, Nickolay. Remark on the null-condition for the nonlinear wave equation. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 135-145. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_1_135_0/

[1] Choquet-Bruhat, Y.-De Witt-Morette, Cécile, Analysis, Manifolds and Physics, Part 2, North-Holland (1989). | Zbl 0682.58002

[2] Choquet-Bruhat, Y.-Christodoulou, D., Existence of global solutions of the Yang-Mils, Higgs and spinor field equations in 3+1 dimensions, Ann. E.N.S., 4ème Série, 14 (1981), 481-500. | MR 654209 | Zbl 0499.35076

[3] Christodoulou, D., Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure. Appl. Math., 39 (1986), 267-282. | MR 820070 | Zbl 0612.35090

[4] Georgiev, V., Global solution of the system of wave and Klein-Gordon equations, Math. Z., 203 (1990), 683-698. | MR 1044072 | Zbl 0671.35052

[5] Klainerman, S., The null condition and global existence to nonlinear wave equation, Lectures in Apll. Math., 23 (1986), 293-326. | MR 837683 | Zbl 0599.35105

[6] Klainerman, S., Remarks on the global Sobolev inequalities in the Minkovski space Rn+1, Comm. Pure Appl. Math., 40 (1987), 111-117. | MR 865359 | Zbl 0686.46019

[7] Penrose, R., Conformal treatment of infinity in relativity, groups and topology, B. De Witt and C. De Witt (eds.), Gordon and Breach (1963). | MR 195547 | Zbl 0148.46403