相关论文: Global existence of small amplitude solutions to o…
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 Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional…
We consider the initial value problem for a system of cubic nonlinear Schr\"odinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses satisfying the resonance relation. We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at…
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…
We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…
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 consider the Cauchy problem for cubic nonlinear Klein-Gordon equations in one space dimension. We give the $L^p$-decay estimate for the small data solution and show that it decays faster than the free solution if the cubic nonlinearity…
We shall be concerned with the Cauchy problem for quasilinear systems in three space dimensions of the form \label{i.1} \partial^2_tu^I-c^2_I\Delta u^I = C^{IJK}_{abc}\partial_c u^J\partial_a\partial_b u^K + B^{IJK}_{ab}\partial_a…
In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in $\R^3$. By making use of Bourgain's method in conjunction with a precise Strichartz estimate of S.Klainerman and D.Tataru, we…
In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with…
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…
Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\Box u + u = P (u, $\partial$\_t u, $\partial$\_x u; $\partial$\_t $\partial$\_x u, $\partial$^2\_x u)$ , where P is a homogeneous polynomial of degree…
In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…
In the paper we consider the nonexistence of global solutions of the Cauchy problem for coupled Klein-Gordon equations of the form \begin{eqnarray*} \left\{\begin{array}{l} u_{tt}-\Delta u+m_1^2 u+K_1(x)u=a_1|v|^{q+1}|u|^{p-1}u…
We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time…
We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…