103 citations · 425 across the 52 of their papers we have counts for
55 papers
Low-regularity invariant measure for the complex-valued mKdV
Zachary Lee, Nataša Pavlović, Gigliola Staffilani +1
In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an…
Quasi invariant Gaussian measures for the nonlinear Schrödinger equation on
Leonardo Tolomeo, Nicola Visciglia
We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schrödinger equation posed on . In partic…
Well-posedness and invariant measures for complex valued modified KdV equation
Carlos E. Kenig, Andrea R. Nahmod, Nataša Pavlović +2
We consider the one dimensional periodic complex valued mKdV, which corresponds to the first equation above cubic NLS in the associated integrable hierarchy. Our main result is the…
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…
Global -solutions for the generalized derivative NLS on
Masayuki Hayashi, Tohru Ozawa, Nicola Visciglia
We prove global existence of solutions to the Cauchy problem for the generalized derivative nonlinear Schrödinger equation on the 1-d torus. This answers an open problem pose…
Almost surely smoothed scattering for cubic NLS
Nicolas Burq, Herbert Koch, Nicola Visciglia +1
We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing…