Existence and a priori bounds for electrostatic Klein-Gordon-Maxwell systems in fully inhomogeneous spaces
Olivier Druet, Emmanuel Hebey
在紧致黎曼流形的非齐次背景下，证明了当质量势（由相位平衡）在量化意义下很小时，静电Klein-Gordon-Maxwell系统的存在性和一致有界性.
We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense.
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In this note, we consider discrete nonlinear Klein-Gordon equations with potential. By the pioneering work of Sigal, it is known that for the "continuous" nonlinear Klein-Gordon equation, no small time periodic solution exists generically. However, for the discrete nonlinear Klein-Gordon equations, we show that there exist small time periodic solutions.
We prove global well-posedness for the 3D Klein-Gordon equation with a concentrated nonlinearity.
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 will be adapted to this $2+1$ dimensional case.
On the stability of standing waves of Klein-Gordon equations in a semiclassical regime
研究了两类Klein-Gordon方程在半经典区域的驻波的轨道稳定性和不稳定性。
On dispersion for Klein Gordon equation with periodic potential in 1D
利用已有的Bloch函数的估计，我们证明了一维空间中具有时间无关的周期位势和一般质量的Klein-Gordon方程的衰变估计
In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge) standing waves, having the phase corresponding to the mass coefficient in the Klein-Gordon Lagrangian.
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 standing waves.
Klein-Gordon-Maxwell equations in high dimensions
证明了高维静电Klein-Gordon-Maxwell方程组山路解的存在性和先验有界性。
We consider the decay rate of solutions to nonlinear Klein-Gordon systems with a critical type nonlinearity. We will specify the optimal decay rate for a specific class of Klein-Gordon systems containing the dissipative nonlinearites. It will turn out that the decay rate which is previously found in some models is optimal.
On the orbital stability of standing-waves solutions to a coupled non-linear Klein-Gordon equation
考虑两个耦合的非线性Klein-Gordon方程组。我们证明了驻波解的存在性和基态的Lyapunov函数的存在性。
Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds
静态Klein-Gordon-Maxwell-Proca系统是静电Klein-Gordon-Maxwell系统的大规模版本。在这些系统中的向量场继承了质量，并受普罗卡作用量的支配，普罗卡作用量推广了麦克斯韦作用量。根据以前的工作Druet等人。我们证明了存在性和统一的界限，这样的系统在双临界情况下的尺寸4。
On The Convergence of the Variational Iteration Method Applied to Variable Coefficient Klein-Gordon Problems
本文提出适用于变系数Klein-Gordon方程的变分迭代法表述，并证明该方法生成的近似解序列收敛到Airy函数。
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at a given, large time. Moreover, we uncover a significant difference between Klein-Gordon and the wave equation in the low frequency, large time regime, where Klein-Gordon exhibits a worse decay that the wave, unlike in the flat space.
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main new ingredients of our method is an improved linear dispersion estimate exploiting the asymptotic spherical symmetry of Klein-Gordon waves, and a corresponding bilinear oscillatory integral estimate.
Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson
我们证明了在非相对论极限下，在适当的初始条件下，1+3维Klein-Gordon-Maxwell系统的解在能量空间收敛到Schrodinger-Poisson系统的解.这需要将纯量克莱因-戈登场分裂为两个场之和，在物理解释中对应于电子和正电子。
In this paper, we prove the exponential decay of local energy for the Klein-Gordon equation with localized critical nonlinearity. The proof relies on generalized Strichartz estimates, and semi-group of Lax-Phillips.
Global solutions of quasilinear systems of Klein--Gordon equations in 3D
证明了三维空间中不同速度的拟线性Klein-Gordon方程组的小数据整体解的存在性和离散性。作为应用，我们得到了电子Euler-Maxwell方程的一个鲁棒的全局稳定性结果。
Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth
我们得到了在整个空间或在星形障碍物的外部，具有阻尼的非线性Klein-Gordon方程的总能量在空间无穷远处的一致指数衰减。
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 and Klein-Gordon equations in order to get sufficient decay rates when energies are not uniformly bounded. These techniques are compatible with those introduced in previous work on two spatial-dimensional quasi-linear wave-Klein-Gordon systems, and can be applied in much general cases.
Finite time blow-up of semi-linear Klein-Gordon equations with positive initial energy in FLRW spacetimes
针对FLRW时空中半线性Klein-Gordon方程，论文将Minkowski时空的凹性方法推广至该背景，建立了解发生有限时间爆破的充分条件。
We study the Cauchy problem for the Klein-Gordon-Zakharov system in 3D with low regularity data. We lower down the regularity to the critical value with respect to scaling up to the endpoint. The decisive bilinear estimates are proved by means of methods developed by Bejenaru-Herr for the Zakharov system and already applied by Kinoshita to the Klein-Gordon-Zakharov system in 2D.
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.
Asymptotic behavior of small solutions to the Vlasov--Klein--Gordon system in high dimensions
本文研究高维Vlasov-Klein-Gordon系统中小解的渐进行为，采用向量场方法和双曲面叶结构分析，克服Klein-Gordon场质量带来的挑战。
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 linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are established. The results and estimates obtained in this paper will be used to study the interaction of solitons and the stability of multisolitons of nonlinear Klein-Gordon equations.
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 solutions.
We look for three dimensional vortex-solutions, which have finite energy and are stationary solutions, of Klein-Gordon-Maxwell-Proca type systems of equations. We prove the existence of three dimensional cylindrically symmetric vortex-solutions having a least possible energy among all symmetric solutions. Moreover we show that, if the Proca mass disappears, then the solutions tends to a solution of the Klein-Gordon-Maxwell system.
We present a set of time quasi-periodic solutions to a nonlinear Klein-Gordon equation with a decaying nonlinear term on the torus in arbitrary dimensions. This paper generalizes the bifurcation method developed in [W2].
Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetry
我们证明了具有径向对称性的三维Klein-Gordon-Zakharov系统的小能量散射。其证明思想与\cite{GN}中研究的Zakharov系统相同，即结合正规形约化和径向改进的Zakhartz估计
Almost optimal local well-posedness of the Maxwell-Klein-Gordon equations in 1+4 dimensions
我们证明了$\R^{1+4}$上相对于库仑规范的Maxwell-Klein-Gordon方程对于所有$ε> 0$，对于$H^{1+ε}$中的初始数据是局部适定的.这建立在Klainerman和Machedon以前的工作上，他们通过忽略系统的椭圆特征以及立方项，证明了来自Maxwell-Klein-Gordon系统的模型问题的相应结果。
We show the ill-posedness of the Cauchy problem for the Dirac-Klein-Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the regularities for which this problem is well-posed or ill-posed.
This article resolves some errors in the paper "Scattering threshold for the focusing nonlinear Klein-Gordon equation", Analysis & PDE 4 (2011) no. 3, 405-460. The errors are in the energy-critical cases in two and higher dimensions.
Global solutions of the Klein-Gordon - Schroedinger system with rough data
本文证明了具有Yukawa耦合的Klein-Gordon - Schroedinger系统在不一定具有有限能量的粗糙数据下具有唯一的整体解。证明使用了广义双线性估计的Eschenhartz型和Bourgain的想法，将数据分为低，高频率部分。
In this paper, we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is well-posed in $\ell^2(h{\mathbb{Z}}^n).$ However, we also recover the well-posedness results in the certain Sobolev spaces in the limit of the semiclassical parameter $h\rightarrow 0.$
Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions
本文考虑三维空间中具有二次非线性项的波与Klein-Gordon方程耦合系统的Cauchy问题。在一定的条件下，包括波方程之间自相互作用的零条件下，我们证明了小振幅解的整体存在性。对于这类耦合系统，我们的条件比Georgiev引入的强零条件弱得多。因此，我们的结果适用于某些物理系统，如Dirac-Klein-Gordon方程，Dirac-Proca方程和Klein-Gordon-Zakharov方程。
Strong instability of standing waves for a system of nonlinear Klein-Gordon equations with quadratic interaction
研究二维和三维空间中带二次相互作用的非线性Klein-Gordon方程组，在不假设质量共振条件时，证明驻波解的强不稳定性。
Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations
在原点外径向对称的条件下，我们给出了Klein-Gordon方程及其它具有超线性幂非线性项的半线性波动方程的扰动在一维或高维空间中的爆破结果.
This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on real hyperbolic spaces.
On dispersive estimates for one-dimensional Klein-Gordon equations
本文改进了1D Klein-Gordon方程色散衰减的结果，提出新方法以在更强的norm中建立衰减并减弱势函数的假设。
Subcritical and supercritical Klein-Gordon-Maxwell equations without Ambrosetti-Rabinowitz condition
本文给出了非线性Klein-Gordon-Maxwell方程正解和基态解的存在性的一些结果。我们介绍了一个一般的非线性亚临界和超临界增长，不需要通常的Ambrosetti-Rabinowitz条件。证明是基于变分方法和扰动参数。
Low regularity well-posedness for the one-dimensional Dirac - Klein - Gordon system
在一维空间中证明了Dirac - Klein - Gordon方程的局部适定性，其中Dirac部分属于H^{-{1/4}+ε}，Klein - Gordon部分属于H^{{1/4}-ε}（0 < ε< 1/4），以及整体适定性，如果狄拉克部分属于电荷类L^2，而克莱因-戈登部分属于H^k，其中0 < k < 1/2。证明使用一个空的结构，在检测的d 'Ancona，Foschi和Selberg和双线性估计的Bourgain-Klainerman-Machedon型空间的非线性。
We prove global well-posedness and scattering for the massive Dirac-Klein-Gordon system with small initial data of subcritical regularity in dimension three. To achieve this, we impose a non-resonance condition on the masses.
Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications
本文讨论了分数阶Klein-Gordon方程的一些精确结果。通过时空变换，将分数阶Klein-Gordon方程化为分数阶超贝塞尔型方程.利用超Bessel算子的分数次幂的McBride理论，我们找到了一个精确的分析解.在线性色散波方程的框架内，这些结果的讨论。在高维情形下，给出了分数阶Klein-Gordon方程的精确解.最后，我们提出了一种求具有幂律非线性项的分数阶Klein-Gordon方程行波解的方法。
Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case
在三维径向情形下，我们考虑了Klein-Gordon-Zakharov系统基态能量以下的整体动力学，得到了散射和有限时间爆破的二分法。
Weighted Energy Decay for 3D Klein-Gordon Equation
我们得到了具有一般势的三维Klein-Gordon方程的解在加权能量范数下的色散长时间衰减。这种衰变推广了Jensen和Kato对3D Schredinger方程的结果。为了证明，我们修改了Jensen和Kato的谱方法，使其适用于相对论方程。
We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the $\mathbf{U}(1)$-invariant Klein--Gordon equation in one spatial dimension coupled to an anharmonic oscillator. We also give the complete analysis of the spectrum of the linearization at a solitary wave.
We prove scattering of solutions below the energy norm of the 3D Klein-Gordon equation for 5>p>3. In order to do that, we generate an exponential-type decay estimate in H^{s}, s<1, by means of concentration and a low-high frequency decomposition.
We study the nonlinear Klein-Gordon equation on a product space $M=\R\times X$ with metric $\tilde{g}=dt^2-g$ where $g$ is the scattering metic on $X$. We establish the global-in-time Strichartz estimate for Klein-Gordon equation without loss of derivative by using the microlocalized spectral measure of Laplacian on scattering manifold showed in \cite{HZ} and a Littlewood-Paley squarefunction estimate proved in \cite{Zhang}. We prove the global existence and scattering for a family of nonlinear Klein-Gordon equations for small initial data with minimum regularity on this setting.
Global Existence for Coupled 3-D Nonlinear Wave and Klein-Gordon Equations with Large Derivatives of Initial Data
该研究针对带二次非线性项的三维波动与Klein-Gordon耦合方程的柯西问题，在大导数初始数据、零条件等假设下证明了解的全局存在性，推进了相关偏微分方程理论研究。
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class solutions which are formally asymptotically in $L^2(\mathbb{R})$. A precise rate of convergence is also obtained assuming more regularity.
A Blowup Solution of Multispeed Klein-Gordon System in Space Dimension Two with Small Initial Data
本文构造特殊色散关系并迭代剖面，证明二维多速Klein-Gordon系统小初值全局存在性中(1.2)第一个非退化条件的必要性，并给出有限时间爆破的例子。
Global well-posedness for the Maxwell-Klein Gordon equation in 4+1 dimensions. Small energy
我们证明了R4+1上的临界Maxwell-Klein Gordon方程对于能量较小的光滑初始数据是全局适定的。这减少了大的、平滑的初始数据的全局规律性的问题，从而排除了能量的集中。
We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in $\mathbb{R}^{2+1}$. We want to establish the small data global existence result, and in addition, we also demonstrate the pointwise asymptotic behaviour of the solution to the coupled system. The initial data are not required to have compact support, and this is achieved by applying the Alinhac's ghost weight method to both the wave and the Klein-Gordon equations.
This is the first of the two papers devoted to the study of global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a $U(1)\times \mathbb{R}$ isometry group. In this first part, we reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1 dimensional system. Then, we will give energy estimates and construct the null coordinate system, under which we finally show that the first possible singularity can only occur at the axis.
The Cauchy problem for the Klein-Gordon equation under the quartic potential is considered in the de Sitter spacetime. The existence of the global solution is shown based on the mechanism of the spontaneous symmetry breaking for the small positive Hubble constant. The effects of the spatial expansion and contraction on the problem are considered.
In this paper we consider a Klein-Gordon model with time-dependent periodic coefficients. The aim is to investigate how the presence of the mass term influences energy estimates with respect to the case of vanishing mass, already treated in [18]. The approach is based on a diagonalisation argument for high frequencies and a contradiction argument for bounded frequencies.
Using the hyperboloidal foliation method, we establish stability results for a coupled wave-Klein-Gordon system with quadratic nonlinearities. In particular, we investigate quadratic wave-Klein-Gordon interactions in which there are no derivatives on the massless wave component. By combining hyperboloidal energy estimates with appropriate transformations of our fields, we are able to show global existence of solutions for sufficiently small initial data.
The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations can be shown for two symmetric solutions.
Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system
证明了（2+1）、（3+1）和（4+1）维Klein-Gordon-Schroedinger系统以及（2+1）和（3+1）维Zakharov系统的正则整体解的空间Sobolev范数至多多项式增长，其界依赖于数据的正则类.证明采用傅立叶限制范数方法。
We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations with nonlinearities violating the null conditions. Without the compactness assumptions on the initial data, we aim to establish the existence of small global solutions, and in addition, we want to illustrate the optimal pointwise decay of the solutions. Furthermore, we show that the Klein-Gordon part of the system enjoys linear scattering while the wave par…
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