Related papers: The cubic Dirac equation: Small initial data in $H…

We establish global well-posedness and scattering for the cubic Dirac equation for small data in the critical space $H^1(\mathbb{R}^3)$. The main ingredient is obtaining a sharp end-point Strichartz estimate for the Klein-Gordon equation.…

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 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 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 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 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 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…

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…

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…

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…

We show that the cubic Dirac equation with zero mass is globally well-posed for small data in the scale invariant space H^{\frac{n-1}{2}}(R^n) for n=2, 3. The proof proceeds by using the Fierz identities to rewrite the equation in a form…

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…

The Cauchy problem for the cubic nonlinear Dirac equation in two space dimensions is locally well-posed for data in H^s for s > 1/2. The proof given in spaces of Bourgain-Klainerman-Machedon type relies on the null structure of the…

In this paper, we consider the question of the global well-posedness and scattering for the cubic Klein-Gordon equation $u_{tt}-\Delta u+u+|u|^2u=0$ in dimension $d\geq5$. We show that if the solution $u$ is apriorily bounded in the…

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…

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…

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…

The solution of the Dirac - Klein - Gordon system in two space dimensions with Dirac data in H^s and wave data in H^{s+1/2} x H^{s-1/2} is uniquely determined in the natural solution space C^0([0,T],H^s) x C^0([0,T],H^{s+\frac1/2}),…

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…