Related papers: On turbulence for spacetimes with stable trapping
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent spacetimes. We assume that the solution to the linear…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…
Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the splitting of singular points and their short…
Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws…
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. So far, nonlinear stability of such…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term.…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
In this paper, we analyze the long-time dynamics of small solutions to the $1d$ cubic nonlinear Schr\"odinger equation (NLS) with a trapping potential. We show that every small solution will decompose into a small solitary wave and a…
This paper is concerned with the global stability of the plane wave solutions to the relativistic string equation with non-small perturbations. Under certain decay assumptions on the plane wave, we conclude that the perturbed system admits…
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 study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be…
We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative…
Generic scalar perturbations on a fixed slowly rotating Kerr-AdS black hole background exhibit stable trapping, that is, the scalar field remains in a region between the exterior of the black hole and the AdS boundary for a very long time,…
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.…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
We prove the global leading-order late-time asymptotic behaviour of solutions to inhomogeneous wave equations on dynamical black hole exterior backgrounds that settle down to Schwarzschild backgrounds with arbitrarily small decay rates. In…
We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole…