4 citations · 7 across the 11 of their papers we have counts for
12 papers
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…
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…
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…
Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic -model
Ruoyuan Liu, Nikolay Tzvetkov, Yuzhao Wang
We study the fractional -measure (with order ) and the dynamical problem of its canonical stochastic quantization: the three-dimensional stochastic damped fractional n…
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…
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…
On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation
V. Georgiev, N. Tzvetkov, N. Visciglia
We prove that the solution map associated with the half-wave cubic equation in the periodic setting cannot be uniformly continuous on bounded sets of the periodic Sobolev spac…
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…
Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
N. Tzvetkov, N. Visciglia
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono eq…