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Consequences of the choice of a particular basis of $L^2(S^3)$ for the cubic wave equation on the sphere and the Euclidean space
1. | University of Cergy-Pontoise, UMR CNRS 8088, F-95000 Cergy-Pontoise, France |
References:
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N. Burq and G. Lebeau, Injections de Sobolev Probabilistes et Applications, preprint. |
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N. Burq and N. Tzvetkov, Probabilistic well-posedness for the cubic wave equation, preprint. |
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Nicolas Burq and Nikolay Tzvetkov, Random data Cauchy theory for supercritical wave equations. I. Local theory, Invent. Math., 173 (2008), 449-475.
doi: 10.1007/s00222-008-0124-z. |
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D. Christodoulou, Global solutions of non linear hyperbolic equations for small initial data, Comm. Pure. Appl. Math., 39 (1986), 267-282.
doi: 10.1002/cpa.3160390205. |
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A-S. de Suzzoni, Large data low regularity scattering results for the wave equation on the Euclidian space, Comm. PDE, 38 (2013), 1-49.
doi: 10.1080/03605302.2012.736910. |
[6] |
X. Fernique, R\'egularit\'e des trajectoires des fonctions al\'eatoires gaussiennes, Ecole d’\'et\'e St. Flour. {IV}-1974, Lecture Notes in Math., 480 (1975), 1-96. |
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Michel Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, vol. 89, American Mathematical Society, Providence, RI, 2001. |
[8] |
N. Tzvetkov, Remark on the Null-condition for the nonlinear wave equation, Bollettino U.M.I., 8 (2000), 135-145. |
show all references
References:
[1] |
N. Burq and G. Lebeau, Injections de Sobolev Probabilistes et Applications, preprint. |
[2] |
N. Burq and N. Tzvetkov, Probabilistic well-posedness for the cubic wave equation, preprint. |
[3] |
Nicolas Burq and Nikolay Tzvetkov, Random data Cauchy theory for supercritical wave equations. I. Local theory, Invent. Math., 173 (2008), 449-475.
doi: 10.1007/s00222-008-0124-z. |
[4] |
D. Christodoulou, Global solutions of non linear hyperbolic equations for small initial data, Comm. Pure. Appl. Math., 39 (1986), 267-282.
doi: 10.1002/cpa.3160390205. |
[5] |
A-S. de Suzzoni, Large data low regularity scattering results for the wave equation on the Euclidian space, Comm. PDE, 38 (2013), 1-49.
doi: 10.1080/03605302.2012.736910. |
[6] |
X. Fernique, R\'egularit\'e des trajectoires des fonctions al\'eatoires gaussiennes, Ecole d’\'et\'e St. Flour. {IV}-1974, Lecture Notes in Math., 480 (1975), 1-96. |
[7] |
Michel Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, vol. 89, American Mathematical Society, Providence, RI, 2001. |
[8] |
N. Tzvetkov, Remark on the Null-condition for the nonlinear wave equation, Bollettino U.M.I., 8 (2000), 135-145. |
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