相关论文: Global solutions to the eikonal equation
We present an analysis of the stability spectrum for all stationary periodic solutions to the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about…
We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is…
In \cite{poiret}, we explain how we can construct global solutions for the cubic Schr\"odinger equation in three dimensional with initial data in $ L^2(\mathds{R}^3) $. The main ingredient of this proof is the existence of the bilinear…
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…
In this article we study a system of eikonal equations. Our aim is to isolate the solutions which minimise the discontinuity set of the gradient.
In this article, we prove the (uniform) global exponential stabilization of the cubic defocusing Schr\"odinger equation on the torus d-dimensional torus, for d=1, 2 or 3, with a linear damping localized in a subset of the torus satisfying…
In this article we prove that 2-soliton solutions of the sine-Gordon equation (SG) are orbitally stable in the natural energy space of the problem. The solutions that we study are the {\it 2-kink, kink-antikink and breather} of SG. In order…
We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Instead of a vector field grad u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove existence…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…
We consider axisymmetric Euler flows without swirl in $\mathbb{R}^{d}$ with $d\geq 4$, for which the global regularity of smooth solutions is an open problem. When $d = 4$, we obtain global regularity under the assumption that the initial…
We prove the global well-posedness and scattering for the 3D incompressible Euler-Coriolis system with sufficiently small, regular and suitably localized initial data. Equivalently, we obtain the asymptotic stability for "rigid body"…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…
We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may have…
In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by…
We prove a definitive theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex…
We propose a space-time isogeometric finite element method for the linear Schr\"odinger equation, and establish its unconditional stability through a matrix-based analysis. Although maximal-regularity splines in time provide higher accuracy…
On a smooth, closed Riemannian manifold $\left(M,g\right)$ of dimension $n\ge3$, we consider the stationary Schr\"odinger equation $\Delta_gu+h_0u=\left|u\right|^{2^*-2}u$, where $\Delta_g:=-\text{div}_g\nabla$, $h_0\in C^1\left(M\right)$…