Related papers: Scattering for radial energy-subcritical wave equa…

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the…

We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations of Minkowski space, by establishing the first explicit…

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…

In this paper, we study the well-posedness theory and the scattering asymptotics for the energy-critical, Schr\"odinger equation with indefinite potential \begin{equation*} \left\{\begin{array}{l} i \partial_t u+\Delta u-V(x)u…

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2…

We prove scattering for a massless wave equation which is critical in two space dimensions. Our method combines conformal inversion with decay estimates from Struwe's previous work on global existence of a similar equation.

In this paper we prove that the energy - critical nonlinear Schr{\"o}dinger equation in the domain exterior to a convex obstacle is globally well - posed and scattering for initial data having finite energy. To prove this we utilize…

We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…

In this paper, we study the blow up and scattering result of the solution to the focusing nonlinear Hartree equation with potential $$i\partial_t u +\Delta u - Vu = - (|\cdot|^{-3} \ast |u|^2)u, \qquad (t, x) \in \mathbb{R} \times…

We consider the fractional nonlinear Schr\"odinger equation (FNLS) with general dispersion $|\nabla|^\alpha$ and focusing energy-critical nonlinearities $-|u|^\frac{2\alpha}{d-\alpha}u$ and $-(|x|^{-2\alpha} * |u|^2) u$. By adopting…

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in…

We consider the Cauchy problem for (energy-subcritical) nonlinear Schr\"odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum…

In this paper, we investigate the global well-posedness and scattering theory for the defocusing nonlinear Schr\"odinger equation $iu_t + \Delta_\Omega u = |u|^\alpha u$ in the exterior domain $\Omega$ of a smooth, compact and strictly…

We consider the following fractional NLS with focusing inhomogeneous power-type nonlinearity $$i\partial_t u -(-\Delta)^s u + |x|^{-b}|u|^{p-1}u=0,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^N,$$ where $N\geq 2$, $1/2<s<1$, $0<b<2s$ and…

We consider the scattering results of the radial solutions below the ground state to the focusing inhomogeneous nonlinear Schr\"odinger equation $$i\partial_tu+\Delta u +|x|^{-b}|u|^{p}u=0$$ in two dimension, where $0<b<1$ and…

In this paper we prove global well-posedness for the defocusing, energy-subcritical, nonlinear wave equation on $\mathbb{R}^{1 + 3}$ with initial data in a critical Besov space. No radial symmetry assumption is needed.

We consider the NLS with variable coefficients in dimension $n\ge3$ \begin{equation*} i \partial_t u - Lu +f(u)=0, \qquad Lv=\nabla^{b}\cdot(a(x)\nabla^{b}v)-c(x)v, \qquad \nabla^{b}=\nabla+ib(x), \end{equation*} on $\mathbb{R}^{n}$ or more…

In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…

In this paper we study the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schr\"{o}dinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our…