Related papers: Parametrix for wave equations on a rough backgroun…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled…
We establish sharp regional observability results for solutions of the wave equation in a bounded domain of $\Omega \subset \mathbb{R}^n$, in case where the geometric control condition is not satisfied. Assuming that the waves are observed…
In recent years, several pulsar timing array collaborations have reported first hints for a stochastic gravitational wave background at nano-Hertz frequencies. Here we elaborate on the possibility that this signal comes from new physics…
In this paper, for a family of second-order parabolic system or equation with rapidly oscillating and time-dependent periodic coefficients over rough boundaries, we obtain the large-scale boundary estimates, by a quantitative approach. The…
The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…
This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions…
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial conditions pose significant challenges, often leading to a…
This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…
Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$ admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation…
We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…
The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general…
Recently Einstein's invariance of the phase of a plane wave (1905) has been described as "questionable" (Huang). Another definition of this phase, taking into account a "relativistically induced optical anisotropy" for isotropic medium in…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial \Omega)\rightarrow H^1(\partial \Omega)$ (where $\partial\Omega$ is the…