Related papers: A note on the null condition for quadratic nonline…
We prove an abstract result of almost global existence of small solutions to semi-linear Hamiltonian partial differential equations satisfying very weak non resonance conditions and basic multilinear estimates. Thanks to works by…
We consider the Cauchy problem for the system of elastodynamic equations in two dimensions. Specifically, we focus on materials characterized by a null condition imposed on the quadratic part of the nonlinearity. We can construct non-zero…
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
Considered herein is a particular nonlinear dispersive stochastic system consisting of Dirac and Klein-Gordon equations. They are coupled by nonlinear terms due to the Yukawa interaction. We consider a case of homogeneous multiplicative…
In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space $\mathbb{R}^{2}\times \mathbb{T}$, we focus on the lower bound of the lifespan of the smooth solution. When the size of…
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…
In this work, we prove global well-posedness and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity…
This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…
We are interested in the global solutions to a class of Klein-Gordon equations, and particularly in the unified time decay results with respect to the possibly vanishing mass parameter. We give for the first time a rigorous proof, which…
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space $H^1(\mathbb{R})…
We consider the Cauchy problem of systems of quasilinear wave equations in 2-dimensional space. We assume that the propagation speeds are distinct and that the nonlinearities contain quadratic and cubic terms of the first and second order…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1 + n}$ to the unit sphere $\mathbb{S}^2$, which obey a system of non-linear wave equations. The nonlinearity enjoys…
We construct bounded classical solutions of the Boltzmann equation in the whole space without specifying any limit behaviors at the spatial infinity and without assuming the smallness condition on initial data. More precisely, we show that…
We study the initial value formulation of metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field acting as source of the field equations. Sufficient conditions for the well-posedness of the Cauchy problem are formulated. This…
We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in H1. Depending on the character of the nonlinear terms, existence of the large-norm solutions can be extended for all…
We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1D is globally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor and positive index for the scalar field. The main ingredient in…
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…
In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static…