Related papers: Conditional large data scattering results for the …
We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order…
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to…
In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…
We investigate the long-time behavior of solutions with small initial data to the viscoelastic Klein-Gordon equation with general smooth nonlinearity. Our analysis relies on the space-time resonances method to eliminate all nonresonant…
From the work on the weak-null condition by Lindblad and Rodnianski, it is well-known that `bad' quadratic sourcing terms are allowed to appear in coupled semilinear wave equations in three spatial dimensions, provided that such terms…
We study small data scattering of solutions to Nonlinear Klein-Gordon equations with suitable pure power nonlinearities, posed on $\mathbb{R}^d\times \mathcal{M}^k$ with $k\leq2$ and $d\geq1$ and $\mathcal{M}^k$ a compact Riemannian…
In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…
We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some form of the Schr"odinger equation. We consider in particular…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
We consider the problem of scattering for the long range critical nonlinear Klein-Gordon in one space dimension.
In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…
We provide a new analysis of the Boltzmann equation with constant collision kernel in two space dimensions. The scaling-critical Lebesgue space is $L^2_{x,v}$; we prove global well-posedness and a version of scattering, assuming that the…
Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…
We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1+3 dimensions is locally well-posed in a range of Sobolev spaces for the Dirac spinor and the meson field. The result contains and extends the earlier known…
We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove…
In the previous work, we classified the solutions to a family of systems of Klein-Gordon equations with non-negative energy below the ground state into two parts: one blows up in finite time while the other extends to a global solution. In…
In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $\mathbb{S}^3$ and $\mathbb{H}^3$. In…
In this paper we study the global existence and uniqueness of solution for a Klein-Gordon equations system with mixed boundary conditions. Also we analyze the asymptotic behavior of this solution.
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 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…