Related papers: Global existence for some 4-D quasilinear wave equ…
We study the Cauchy problem for 3-D nonlinear elastic waves satisfying the null condition with low regularity initial data. In the radially symmetric case, we prove the global existence of a low regularity solution for every small data in…
We prove global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation.…
In this paper, we establish the global existence of smooth solutions to general 4D quasilinear wave equations satisfying the first null condition with the short pulse initial data. Although the global existence of small data solutions to 4D…
The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations satifying the null condition in an exterior domain. The novelty of our proof is to avoid completely the scaling operator…
We study the global existence of solutions to semilinear damped wave equations in the scattering case with derivative power-type nonlinearity on (1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea is to exploit…
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and…
We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild-de Sitter black hole backgrounds, for appropriately small initial data. The core of the argument is…
We consider the problem of small data global existence for a class of semilinear wave equations with null condition on a Lorentzian background $(\mathbb{R}^{3+1}, g)$ with a \textbf{time dependent metric $g$} coinciding with Minkowski…
We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a…
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…
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…
We consider quasilinear wave equations in $(1+3)$-dimensions where the nonlinearity $F(u,u',u")$ is permitted to depend on the solution rather than just its derivatives. For scalar equations, if $(\partial_u^2 F)(0,0,0)=0$, almost global…
In this article one will develop a new type of energy method based on a foliation of spacetime into hyperboloidal hypersurfaces . As we will see, with this method, some classical results such as global existence and almost global existence…
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 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 consider the problem of small data global existence for quasilinear wave equations with null condition on a class of Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with \textbf{time dependent} inhomogeneous metric. We show that…
We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We show that for homogeneous Dirichlet boundary values and sufficiently…
We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…
We show global existence of small solutions to the Cauchy problem for a system of quasi-linear wave equations in three space dimensions. The feature of the system lies in that it satisfies the weak null condition, though we permit the…