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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 regularity on the corresponding Radon–Nikodym density, as well as new bounds on the growth of the Sobolev norms of the solutions.
@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'I.H.P. Analyse non lin\'eaire},
pages = {863--917},
volume = {40},
number = {4},
year = {2023},
doi = {10.4171/aihpc/62},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/62/}
}
TY - JOUR AU - Planchon, Fabrice AU - Tzvetkov, Nikolay AU - Visciglia, Nicola TI - Modified energies for the periodic generalized KdV equation and applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 863 EP - 917 VL - 40 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/62/ DO - 10.4171/aihpc/62 LA - en ID - AIHPC_2023__40_4_863_0 ER -
%0 Journal Article %A Planchon, Fabrice %A Tzvetkov, Nikolay %A Visciglia, Nicola %T Modified energies for the periodic generalized KdV equation and applications %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 863-917 %V 40 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/62/ %R 10.4171/aihpc/62 %G en %F AIHPC_2023__40_4_863_0
Planchon, Fabrice; Tzvetkov, Nikolay; Visciglia, Nicola. Modified energies for the periodic generalized KdV equation and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 4, pp. 863-917. doi: 10.4171/aihpc/62
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