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.

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

References in corpus (2)

• Quasi-invariant gaussian measures for one dimensional Hamiltonian PDE's
• Blow up for the critical gKdV equation III: exotic regimes