Related papers: Decay estimates for the one-dimensional wave equat…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
The behavior of isothermal plasma waves has been analyzed near the Schwarzschild horizon. We consider a non-rotating background with non-magnetized and magnetized plasmas. The general relativistic magnetohydrodynamical equations for the…
We find broad classes of exact 4-dimensional asymptotically flat black hole solutions in Einstein-Maxwell theories with a non-minimally coupled dilaton and its non-trivial potential. We consider a few interesting limits, in particular, a…
In this paper, we study the precise decay rate in time to solutions of the Cauchy problem for the one-dimensional conservation law with a nonlinearly degenerate viscosity where the far field states are prescribed. Especially, we deal with…
We consider the following family of Cauchy problems: {equation*} i\partial_t u= \Delta u - u|u|^\alpha, (t,x) \in \R \times \R^d {equation*} $$u(0)=\varphi\in H^1(\R^d)$$ where $0<\alpha<\frac 4{d-2}$ for $d\geq 3$ and $0<\alpha<\infty$ for…
We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the…
The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by…
We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form $|x|^{-\alpha}$ or $|(x,t)|^{-\alpha}$. In particular, we show that space-time weights $|(x,t)|^{-\alpha}$ admit stronger…
The decay of massive scalar field in the Schwarzschild black hole background is investigated here by consideration its quasinormal spectrum. It has been proved that the so-called $quasi-resonant$ modes, which are arbitrary long living…
In this paper we prove convergence to a steady state as $t\to\infty$ for solutions to the subdiffusion equation \[ \partial_t^\alpha u - \mathbb{L} u = q(x)u - p(x)f(u) + r \] with the exponential ($\alpha=1$) or power law…
We present an analytic method for calculating the late-time tails of a linear scalar field outside a Kerr black hole. We give the asymptotic behavior at timelike infinity (for fixed $r$), at future null infinity, and along the event horizon…
We are concerned with the Sturm-Liouville problem on the half line. We show that when the potential $q$ is subject only to power decay at infinity the $L^2$ solution may be continued into a sector of the so-called un-physical sheet. This…
In this paper, with considering the nonlinear electromagnetic field coupled to Einstein gravity, we obtain the higher dimensional slowly rotating charged black hole solutions. By use of the fact that the temperature of the extreme black…
We obtain large time decay estimates on weighted $L^p$ spaces for solutions to the wave equation with real-valued potential $V(x)=O(|x|^{-2-a})$, $a>0$, for $|x|>1$.
In this paper we consider the local energy decay result for wave equations with a short-range potential. It is important to note that one never uses a finite speed of propagation property unlike the historical previous papers. The essential…
We study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with…
In this paper, a class of variable-coefficient wave equations equipped with time-dependent damping and the nonlinear source is considered. We show that the total energy of the system decays to zero with an explicit and precise decay rate…
We investigate the backreaction equations for an acoustic black hole formed in a Laval nozzle under the assumption that the motion of the fluid is one-dimensional. The solution in the near-horizon region shows that as phonons are…
This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $d+1$, $d\ge3$, the local energy of solutions to the scalar wave equation…
We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviours, at the horizon and at infinity, of vortex solutions for the gauge…