Related papers: Quasilinear wave equations on Schwarzschild-de Sit…
We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…
We revisit global existence and decay for small-data solutions of semilinear wave equations on extremal Reissner-Nordstr\"om black hole backgrounds satisfying the classical null condition, a problem which was previously addressed by the…
In this paper, we consider the propagation of waves in the space-time of a single black hole with a static Schwarzschild radius in the expanding universe, namely, the solutions of the linear and semilinear Klein-Gordon equations.
In the presence of confinement, small-data solutions to nonlinear dispersive equations can exhibit a gradual energy transfer from low to high frequencies, a mechanism driving the emergence of weakly turbulent dynamics. We show that such a…
In this paper, we study the long time dynamics of solutions to the defocusing semilinear wave equation $\Box_g\phi=|\phi|^{p-1}\phi$ on the Schwarzschild black hole spacetimes. For $\frac{1+\sqrt{17}}{2}<p<5$ and sufficiently smooth and…
We explore the global existence of solutions to systems of quasilinear wave equations satisfying the null condition when the initial data are sufficiently small. We adapt an approach of Keel, Smith, and Sogge, which relies on integrated…
The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on…
We study in special limiting cases quasinormal modes of massive scalar fields in the Schwarzschild-de Sitter black hole backgrounds. We determine the lower limit on the mass parameter of the scalar field that allows the waves with…
This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…
We consider a system of quasilinear wave equations on the product space $\mathbb{R}^{1+3}\times \mathbb{S}^1$, which we want to see as a toy model for Einstein equations with additional compact dimensions. We show global existence for small…
It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the…
We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…
This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, asymptotically flat, and notably, non-stationary spacetimes.…
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.
The central equations in classical general relativity are the Einstein Field Equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more…
We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity.…
We present the first rigorous study of nonlinear wave equations on extremal black hole spacetimes without any symmetry assumptions on the solution. Specifically, we prove global existence with asymptotic blow-up for solutions to nonlinear…
Conformally invariant scalar waves in black hole spacetimes which are asymptotically anti-de Sitter are investigated. We consider both the $(2+1)$-dimensional black hole and $(3+1)$-dimensional Schwarzschild-anti-de Sitter spacetime as…