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-Nykodim density, as well as new bounds on the growth of the Sobolev norms of the solutions.

Modified energies for the periodic generalized KdV equation and applications

Nicola Visciglia
Ultimo
2022-01-01

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 $L^q$ regularity on the corresponding Radon-Nykodim density, as well as new bounds on the growth of the Sobolev norms of the solutions.
2022
Planchon, Fabrice; Tzvetkov, Nikolay; Visciglia, Nicola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1136279
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