相关论文: Scattering and small data completeness for the cri…
We give a short description of the proof of asymptotic-completeness for NLS-type equations, including time dependent potential terms, with radial data in three dimensions. We also show how the method applies for the two-body Quantum…
We consider the mass-subcritical nonlinear Schr\"odinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $s_c\in(\max\{-1,-\frac{d}{2}\},0)$, we prove that any solution…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
We prove a modified scattering and asymptotic completeness for the derivative nonlinear Schr\"odinger equation. This is the first result proving asymptotic completeness in a quasilinear setting. Our approach combines the method of testing…
We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the…
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in two space dimensions for all powers $p>0$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in…
In this article we study the asymptotic behavior of a quadratic NLS equation with small, time-dependent potential and small spatially localized initial data. We prove global existence and scattering of solutions. The two main ingredients of…
In this paper we consider the long time behavior of solutions to the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times\mathbb{T}^{d}$, $1\leq d\leq4$. For sufficiently small, smooth, decaying data we prove…
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in one space dimension for powers $p>2$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the…
This paper is a continuation of our previous study on the long time behavior of solution to the nonlinear Schr"odinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the…
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to the linear equation possess a particular finite-order…
We prove that under a generic asymptotic condition on the charge, the small data solutions to the Vlasov-Maxwell system do not verify linear scattering. In other words, we show the non-$L^1$ asymptotic completeness of the system. The proof…
The purpose of this paper is to establish a definitive quantitative nonlinear scattering theory for asymptotically de Sitter solutions of the Einstein vacuum equations in $(n+1)$ dimensions with $n\geq4$ even, which are determined by small…
This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schr\"odinger type equations. We give sharp a threshold of scattering versus non-scattering of mass solutions, depending on the source term. This work…
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we…
We consider the cubic defocusing nonlinear Schr\"odinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all…
We study the asymptotic behaviour in time of solutions and the theory of scattering for the modified Schr"odinger map in two space dimensions. We solve the Cauchy problem with large finite initial time, up to infinity in time, and we…
In the article, we prove the large data scattering for two problems, i.e. the defocusing quintic nonlinear Schr{\"o}dinger equation on $\mathbb{R}^2$ $\times$ $\mathbb{T}$ and the defocusing cubic nonlinear Schr{\"o}dinger equation on…
We consider large time asymptotics for damped nonlinear Schr\"{o}dinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its…