Related papers: Scattering for Defocusing generalized Benjamin-Ono…
We study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of the initial data. The random pertubation is defined through a…
We obtain global well-posedness, scattering, and global $L^{10}_{t,x}$ spacetime bounds for energy-class solutions to the quintic defocusing Schr\"odinger equation in $\R^{1+3}$, which is energy-critical. In particular, this establishes…
We consider the defocusing energy-critical Hartree equation $i\pa_tu+\Delta u=(|\cdot|^{-4}\ast|u|^2)u$ in spatial dimension $d=5$ and prove almost sure scattering with initial data $u_0\in H^s_x(\R^5)$ for any $s\in\R$. The proof relies on…
The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context.…
In this paper, we obtain the global well-posedness and scattering for the radial solution to the defocusing conformal invariant nonlinear wave equation with initial data in the critical Besov space…
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…
We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schr\"odinger equations $$ \begin{cases} i\partial_t u_\mu + \Delta u_\mu - \sum_{\mu,\nu=1 }^N…
We consider the defocusing $\dot H^1$-critical nonlinear Schr\"odinger equation in all dimensions ($n\geq 3$) with a quadratic potential $V(x)=\pm \tfrac12 |x|^2$. We show global well-posedness for radial initial data obeying $\nabla…
We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schr\"odinger equations in dimensions $n \geq 3$, for solutions which have large, but finite, energy and large, but finite,…
The Aharonov-Bohm scattering amplitude is calculated in the context of planar gravity with localized sources which also carry a magnetic flux. These sources cause space-time to develop conical singularities at their location, thus…
We study the cubic defocusing nonlinear Schr\"odinger equation on $\mathbb{R}^4$ with supercritical initial data. For randomized initial data in $H^s(\mathbb{R}^4)$, we prove almost sure local wellposedness for $\frac{1}{7} < s < 1$ and…
In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
In this article we study the defocusing energy-critical nonlinear wave equation on $\mathbb{R}^4$ with scaling supercritical data. We prove almost sure scattering for randomized initial data in $H^s(\mathbb{R}^4) \times…
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…
Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature d.c. resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface…
We prove $H^{1}$ scattering for a defocusing NLS on the line with fully variable coefficients. The result is proved by adapting the Kenig--Merle scheme to a non translation invariant setting. In addition, we give an abstract version of the…
We consider the long time dynamics of large solutions to the Benjamin-Ono equation. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times.…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
We consider electronic transport accross one-dimensional heterostructures described by the Dirac equation. We discuss the cases where both the velocity and the mass are position dependent. We show how to generalize the Dirac Hamiltonian in…