相关论文: Asymptotic decay for defocusing semilinear wave eq…

We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In…

In this paper we consider solutions to the linear wave equation on higher dimensional Schwarzschild black hole spacetimes and prove robust nondegenerate energy decay estimates that are in principle required in a nonlinear stability problem.…

We prove that sufficiently regular solutions to the wave equation $\Box_g\phi=0$ on the exterior of the Schwarzschild black hole obey the estimates $|\phi|\leq C_\delta v_+^{-{3/2}+\delta}$ and $|\partial_t\phi|\leq C_{\delta}…

We study the quasilinear wave equation $\Box_{g}\phi=0$ where the metric $g = g(\phi,t,x)$ is close to and asymptotically approaches $g(0,t,x)$, which equals the Schwarzschild metric or a Kerr metric with small angular momentum, as time…

In this paper, we study the asymptotic decay properties for defocusing semilinear wave equations in $\mathbb{R}^{1+2}$ with pure power nonlinearity. By applying new vector fields to null hyperplane, we derive improved time decay of the…

In this paper, we use Dafermos-Rodnianski's new vector field method to study the asymptotic pointwise decay properties for solutions of energy subcritical defocusing semilinear wave equations in $\mathbb{R}^{1+3}$. We prove that the…

We study the massive scalar field equation $\Box_g \phi = m^2 \phi$ on a stationary and spherically symmetric black hole $g$ (including in particular the Schwarzschild and Reissner--Nordstr\"om black holes in the full sub-extremal range)…

This paper is devoted to the study of asymptotic behaviors of solutions to the one-dimensional defocusing semilinear wave equation. We prove that finite energy solution tends to zero in the pointwise sense, hence improving the averaged…

This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…

In recent work, we have proven uniform decay bounds for solutions of the wave equation $\Box_g\phi=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|\phi|\le Cv_+^{-1}$, which holds throughout the domain of…

We present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation $\Box_g \phi = \epsilon \beta^a \partial_a \phi$ on the exterior of the Schwarzschild geometry $(\mathcal{M},g)$.…

In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on…

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 solutions of the scalar wave equation $\Box_g\phi=0$, without symmetry, on fixed subextremal Reissner-Nordstr\"om backgrounds $({\mathcal M}, g)$ with nonvanishing charge. Previously, it has been shown that for $\phi$ arising…

We prove Price's law with an explicit leading order term for solutions $\phi(t,x)$ of the scalar wave equation on a class of stationary asymptotically flat $(3+1)$-dimensional spacetimes including subextremal Kerr black holes. Our precise…

Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately…

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.

Let G(x) be a C^0 function such that |G(x)|\le K|x|^{p} for |x|\le c, for constants K,c>0. We consider spherically symmetric solutions of \Box_g\phi=G(\phi) where g is a Schwarzschild or more generally a Reissner-Nordstrom metric, and such…

We consider the long-time behavior of small amplitude solutions of the semilinear wave equation $\Box \phi =\phi^p$ in odd $d\geq 5$ spatial dimensions. We show that for the quadratic nonlinearity ($p=2$) the tail has an anomalously small…

We consider solutions to the massless Vlasov equation on the domain of outer communications of the Schwarschild black hole. By adapting the r^p-weighted energy method of Dafermos and Rodnianski, used extensively in order to study wave…