200 citations · 1.3k across the 65 of their papers we have counts for
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The Second Picard iteration of NLS on the sphere does not regularize Gaussian random initial data
Nicolas Burq, Nicolas Camps, Mickaël Latocca +2
We consider the Wick ordered cubic Schrödinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the s…
Probabilistic well-posedeness for the nonlinear Schrödinger equation on the sphere I: positive regularities
Nicolas Burq, Nicolas Camps, Chenmin Sun +1
We establish the probabilistic well-posedness of the nonlinear Schrödinger equation on the sphere . The initial data are distributed according to Gaussian meas…
Quasi-invariance of Gaussian measures for the energy critical nonlinear Schr\" odinger equation
Chenmin Sun, Nikolay Tzvetkov
We consider the energy critical nonlinear Schr\" odinger equation with data distributed according to the Gaussian measure with covariance operator , where is t…
New non degenerate invariant measures for the Benjamin-Ono equation
Nikolay Tzvetkov
We show that the recent work by G{é}rard-Kappeler-Topalov can be used in order to construct new non degenerate invariant measures for the Benjamin-Ono equation on the Sobolev space…
Blow-up for the 1D cubic NLS
Valeria Banica, Renato Lucà, Nikolay Tzvetkov +1
We consider the 1D cubic NLS on and prove a blow-up result for functions that are of borderline regularity, i.e. for any for the Sobolev scale and $…
Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space
Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov +1
We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove g…