6 papers · 1 filter
Almost sure global nonlinear smoothing for the 2D NLS
Chenmin Sun, Nikolay Tzvetkov
In this article, we prove an almost-sure global in time nonlinear smoothing effect for NLS on the two-dimensional torus. For deterministic data, this phenomenon was proved for the…
Large torus limit of global dynamics of the two-dimensional dispersive Anderson model
Ruoyuan Liu, Nikolay Tzvetkov
We continue the study of the two-dimensional dispersive Anderson model (DAM), i.e. the nonlinear Schrödinger equation with multiplicative spatial white noise. For this model, globa…
Hyperbolic nonlinear Schrödinger equations on
Engin Başakoğlu, Chenmin Sun, Nikolay Tzvetkov +1
In this paper, we consider the hyperbolic nonlinear Schrödinger equations (HNLS) on . We obtain the sharp local well-posedness up to the critical regula…
Local well-posedness for the periodic Boltzmann equation with constant collision kernel
Engin Başakoğlu, Nikolay Tzvetkov, Chenmin Sun +1
We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain , . Using the existing techniques from nonlinear…
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…
Invariant measures and long time behaviour for the Benjamin-Ono equation II
Nikolay Tzvetkov, Nicola Visciglia
As a continuation of our previous work on the subject, we prove new measure invariance results for the Benjamin-Ono equation. The measures are associated with conservation laws who…