Related papers: The cubic Dirac equation: Small initial data in $H…
Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $H^{\frac12}(\mathbb{R}^2)$ is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein-Gordon…
We consider the Dirac equation with cubic Hartree-type nonlinearity derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data scattering result in full subcritical range. Main ingredients of the proof are the localized…
We study a cubic Dirac equation on $\mathbb{R}\times\mathbb{R}^{3}$ \begin{equation*} i \partial _t u + \mathcal{D} u + V(x) u = \langle \beta u,u \rangle \beta u \end{equation*} perturbed by a large potential with almost critical…
We prove that the initial value problem for the Dirac equation $ \left ( -i\gamma^\mu \partial_\mu + m \right) \psi = \left(\frac{e^{- |x|}}{|x|} \ast ( \overline \psi \psi)\right) \psi \quad \text{in } \ \R^{1+3} $ is globally well-posed…
The aim of this paper is to establish the $L^2_t$-endpoint Strichartz estimate for (half) Klein-Gordon equations on a weakly asymptotically flat space-time. As an application we prove small data global well-posedness and scattering for…
We present some results obtained in collaboration with prof. Piero D'Ancona concerning global existence for the 3D cubic non linear massless Dirac equation with a potential for small initial data in $H^1$ with slight additional assumptions.…
We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for…
We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp pointwise decay results for general cubic nonlinearities without additional structure. We also prove the…
We solve globally a radial cubic Dirac equation perturbed with a small potential, with data of small critical norm $H^{1}$. The main tool are new endpoint estimates of the perturbed Dirac flow for a class of radial-type initial data.
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…
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…
A refined trilinear Strichartz estimate for solutions to the Schr\"odinger equation on the flat rational torus T^3 is derived. By a suitable modification of critical function space theory this is applied to prove a small data global…
We consider the periodic defocusing cubic nonlinear Klein-Gordon equation in three dimensions in the symplectic phase space $H^{\frac{1}{2}}(\mathbb{T}^3) \times H^{-\frac{1}{2}}(\mathbb{T}^3)$. This space is at the critical regularity for…
We consider both the defocusing and focusing cubic nonlinear Klein--Gordon equations $$ u_{tt} - \Delta u + u \pm u^3 =0 $$ in two space dimensions for real-valued initial data $u(0)\in H^1_x$ and $u_t(0)\in L^2_x$. We show that in the…
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.
In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $\dot{H}^{1/2} \times \dot{H}^{-1/2}$. We show that if the initial data is radial and lies in…
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 establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^{2} \times B_{1,1}^{1}$. This space of functions is a scale invariant subspace of $\dot{H}^{1/2} \times…
We obtain conditional results on the global existence and scattering for large solutions of the Dirac-Klein-Gordon system in critical spaces in dimension $1+3$. In particular, for bounded solutions we identify a space-time Lebesgue norm…