Modified energies for the periodic generalized KdV equation and applications

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.

arXiv commentfinal version, to appear in Ann. Inst. Henri Poincaré, Anal. Non Linéaire

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