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arXiv · 2107.01926

Modified energies for the periodic generalized KdV equation and applications

F. Planchon·N. Tzvetkov·N. Visciglia
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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 $L^p$ regularity on the corresponding Radon-Nykodim density, as well as new bounds on the growth of the Sobolev norms of the solutions.

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F. Planchon, N. Tzvetkov, N. Visciglia. 2021-07-05. Modified energies for the periodic generalized KdV equation and applications. https://arxiv.org/abs/2107.01926

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