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 ViscigliaUltimo
2023-01-01
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.File in questo prodotto:
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