2 citations · 3 across the 3 of their papers we have counts for
3 papers
math.AP2024★ 2 cited
New bounds on the high Sobolev norms of the 1d NLS solutions
Diego Berti, Fabrice Planchon, Nikolay Tzvetkov +1
We introduce modified energies that are suitable to get upper bounds on the high Sobolev norms for solutions to the D periodic NLS. Our strategy is rather flexible and allows us…
math.AP2021
Growth of Sobolev Norms for 2d NLS with harmonic potential
F. Planchon, N. Tzvetkov, N. Visciglia
We prove polynomial upper bounds on the growth of solutions to 2d cubic NLS where the Laplacian is confined by the harmonic potential. Due to better bilinear effects our bounds imp…
math.AP2021★ 1 cited
Modified energies for the periodic generalized KdV equation and applications
F. Planchon, N. Tzvetkov, N. Visciglia
We construct modified energies for the generalized KdV equation. As a consequence, we obtain quasi-invariance of the high order Gaussian measures along with regularity on the…