19 citations · 69 across the 23 of their papers we have counts for
25 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…
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…
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…
Weak universality results for a class of nonlinear wave equations
Chenmin Sun, Nikolay Tzvetkov, Weijun Xu
We study the weak universality of the two-dimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of high-degree potentials scaling to the fractional …
Sharp resolvent estimate for the Baouendi-Grushin operator and applications
Victor Arnaiz, Chenmin Sun
In this article we study the semiclassical resolvent estimate for the non-selfadjoint Baouendi-Grushin operator on the two-dimensional torus $\mathbb{T}^2=\mathbb{R}^2/(2π\mathbb{Z…
Sharp decay rate for the damped wave equation with convex-shaped damping
Chenmin Sun
We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a Höl…
Refined probabilistic global well-posedness for the weakly dispersive NLS
Chenmin Sun, Nikolay Tzvetkov
We continue our study of the cubic fractional NLS with very weak dispersion and data distributed according to the Gibbs measure. We construct the natural strong solutions for…
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
Nicolas Burq, Chenmin Sun
We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. We prove that when the damping coefficient is sufficiently smooth (…
Observability of Baouendi-Grushin-Type Equations Through Resolvent Estimates
Cyril Letrouit, Chenmin Sun
In this article, we study the observability (or, equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed o…
Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping
Nicolas Burq, Chenmin Sun
We study the energy decay rate of the Kelvin-Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the s…
Concerning the pathological set in the context of probabilistic well-posedness
Chenmin Sun, Nikolay Tzvetkov
We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set of the Sobolev space of s…
Gibbs measure dynamics for the fractional NLS
Chenmin Sun, Nikolay Tzvetkov
We construct global solutions on a full measure set with respect to the Gibbs measure for the one dimensional cubic fractional nonlinear Schrödinger equation (FNLS) with weak dispe…
Time optimal observability for Grushin Schrödinger equation
Nicolas Burq, Chenmin Sun
We consider two dimensional Grushin Schrödinger equation posed on a finite cylinder $Ω=(-1,1)_x\times \T_y$ with Dirichlet boundary condition. We obtain the sharp observability by…
New examples of probabilistic well-posedness for nonlinear wave equations
Chenmin Sun, Nikolay Tzvetkov
We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures…
Low regularity blowup solutions for the mass-critical NLS in higher dimensions
Chenmin Sun, Jiqiang Zheng
In this paper, we study the -stability of the log-log blowup regime (which has been completely described in a series of recent works by Merle and Raphael) for the focusing mas…
Exact Controllability of linear KP-I equation
Chenmin Sun
We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insur…
Internal controllability of non-localized solution for the Kodomtsev-Petviashvili II equation
Chenmin Sun, Ivonne Rivas
The internal control problem for the Kadomstev-Petviashvili II equation, known as KP-II, is the object of study in this paper. The controllability in from vertical strip i…
On the stabilization of a hyperbolic Stokes system under geometric control condition
Felipe W. Chaves-Silva, Chenmin Sun
In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain…
Semi-classical propagation of singularity for Stokes system
Chenmin Sun
We study the quasi-mode of Stokes system posed on a smooth bounded domain with Dirichlet boundary condition. We prove that the high energy L2 norm of solutions concentrate on the b…
On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation
Chenmin Sun
In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter . When ,we prove…
Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data
Chenmin Sun, Hua Wang, Xiaohua Yao +1
The aim of this note is to adapt the strategy in [4][See,B.Dodson, J.Murphy, a new proof of scattering below the ground state for the 3D radial focusing cubic NLS, arXiv:1611.04195…