no. 4
Modified energies for the periodic generalized KdV equation and applications
Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 40 (2023) no. 4, pp. 863-917
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We construct modified energies for the generalized KdV equation. As a consequence, we obtain quasi-invariance of the high-order Gaussian measures, along with L q regularity on the corresponding Radon–Nikodym density, as well as new bounds on the growth of the Sobolev norms of the solutions.

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DOI : 10.4171/aihpc/62
Classification : 35A01
Keywords: Dispersive partial differential equation, KdV 
@article{AIHPC_2023__40_4_863_0,
     author = {Planchon, Fabrice and Tzvetkov, Nikolay and Visciglia, Nicola},
     title = {Modified energies for the periodic generalized {KdV} equation and applications},
     journal = {Annales de l'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {863--917},
     year = {2023},
     volume = {40},
     number = {4},
     doi = {10.4171/aihpc/62},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/62/}
}
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%A Tzvetkov, Nikolay
%A Visciglia, Nicola
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Planchon, Fabrice; Tzvetkov, Nikolay; Visciglia, Nicola. Modified energies for the periodic generalized KdV equation and applications. Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 40 (2023) no. 4, pp. 863-917. doi: 10.4171/aihpc/62

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