JournalsaihpcVol. 40, No. 4pp. 863–917

Modified energies for the periodic generalized KdV equation and applications

  • Fabrice Planchon

    Sorbonne Université, CNRS, Paris, France

  • Nikolay Tzvetkov

    École Normale Supérieure de Lyon, CNRS, France

  • Nicola Visciglia

    Università Degli Studi di Pisa, Italy
Modified energies for the periodic generalized KdV equation and applications cover
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Abstract

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.

Cite this article

Fabrice Planchon, Nikolay Tzvetkov, Nicola Visciglia, Modified energies for the periodic generalized KdV equation and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 4, pp. 863–917

DOI 10.4171/AIHPC/62