Related papers: On the global regularity for a Wave-Klein-Gordon c…
We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere $\mathbb{S}^m$, $m \geq 1$, and prove global regularity and scattering for classical smooth data of finite energy. In…
This paper is a continuation of a previous work Germain-Pusateri (2020) by the first two authors. We focus on $1$ dimensional quadratic Klein-Gordon equations with a potential, under some assumptions that are less general than…
We prove global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have…
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…
We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global…
The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use compactness arguments and a non-standard analysis to obtain the…
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…
We consider the defocusing nonlinear wave equation of power-type on $\mathbb{R}^3$. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of…
In this article we consider a system of two Klein-Gordon equations, set on the $d$-dimensional box of size $L$, coupled through quadratic semilinear terms of strength $\varepsilon$ and evolving from well-prepared random initial data. We…
In this paper we investigate the rigidity property of a wave component coupled in a wave-Klein-Gordon system. We prove that when the radiation field of the wave component vanishes at the null infinity, the initial data of this component…
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 skew mean curvature flow is an evolution equation for a $d$ dimensional manifold immersed into $\mathbb{R}^{d+2}$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove…
We prove global internal controllability in large time for the nonlinear Schr\"odinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation.…
In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the…
In this paper, we prove global well-posedness and scattering of the Cauchy problem for the elliptic-elliptic Davey-Stewartson system (eeDS) for initial data $u_{0}\in L^{2}(\mathbb{R}^{2})$ in the defocusing case and for $u_{0}\in…
In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly large). This system couples an inviscid transport equation in…
In the previous papers in this series, the global regularity conjecture for wave maps from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic space $\H^m$ was reduced to the problem of constructing a minimal-energy blowup solution…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for…
We critically reexamine the gravitational scattering of scalar particles on a global monopole studied recently. The original investigation of Mazur and Papavassiliou is extended by considering different couplings of the scalar field to the…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…