Related papers: Scattering for the 3D Gross-Pitaevskii equation
We prove small energy scattering for the 3D Klein-Gordon-Zakharov system with radial symmetry. The idea of proof is the same as the Zakharov system studied in \cite{GN}, namely to combine the normal form reduction and the radial-improved…
We study global behavior of small solutions of the Gross-Pitaevskii equation in three dimensions. We prove that disturbances from the constant equilibrium with small, localized energy, disperse for large time, according to the linearized…
We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain…
We prove the small energy scattering for the three-dimensional generalized Zakharov system with radial symmetry based on the idea by Guo and Nakanishi (2014), which treats the usual Zakharov system. For the proof, we use the…
We obtain almost-sure scattering for the cubic defocusing Schr{\"o}dinger equation in the Euclidean space {$\mathbb{R}^3$}, with randomized radially-symmetric initial data at some supercritical regularity scales. Since we make no smallness…
We study the scattering problems for the quadratic Klein-Gordon equations with radial initial data in the energy space. For 3D, we prove small data scattering, and for 4D, we prove large data scattering with mass below the ground state.
The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data…
We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the…
We prove global well-posedness and scattering for the 3D Klein-Gordon-Schr\"odinger system for small radial data in the best known global well-posedness range $(u_0, n_0, n_1)\in L^2\times H^{ -\frac{1}{2} + \epsilon } \times…
We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of…
In this paper we are interested in the global well-posedness of the 3D Klein-Gordon-Zakharov equations with small initial data. We show the uniform boundedness of the energy for the global solution without any compactness assumptions on the…
We consider the Schr{\"o}dinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the…
We consider the Cauchy problem associated with the modified Zakharov-Kuznetsov equation over $\mathbb{R}^2$. Taking into consideration the associated dispersive effects, we introduce, for $s,a\ge 0$, a two-parameter space…
We prove small energy scattering for the 3D Zakharov system with radial symmetry. The main ingredients are normal form reduction and the radial-improved Strichartz estimates.
For $n\geq 3$, we study the Cauchy problem for the fourth order nonlinear Schr\"{o}dinger equations, for which the existence of the scattering operators and the global well-posedness of solutions with small data in Besov spaces…
We study the Cauchy problem for the radial energy critical nonlinear wave equation in three dimensions. Our main result proves almost sure scattering for radial initial data below the energy space. In order to preserve the spherical…
Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and subcritical with respect to…
We study the energy-critical nonlinear Schr\"{o}dinger equation with randomised initial data in dimensions $d>6$. We prove that the Cauchy problem is almost surely globally well-posed with scattering for randomised super-critical initial…
The Cauchy Problem for the modified Zakharov-Kuznetsov equation in three space dimensions is shown to be locally well-posed in $H^s(\R^3)$ for $s > \frac12$. Combined with the conservation of mass and energy this result implies global…
We study the Cauchy problem and the large data $H^1$ scattering for energy subcritical NLS posed on $\R^d\times \T$