ﻻ يوجد ملخص باللغة العربية
We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization for the relevant imaginary multiplicative Gaussian chaos, we prove local well-posedness of SSG for any value of a parameter $beta^2 > 0$ in the nonlinearity. This exhibits sharp contrast with the parabolic case studied by Hairer and Shen (2016) and Chandra, Hairer, and Shen (2018), where the parameter is restricted to the subcritical range: $0 < beta^2 < 8 pi$. We also present a triviality result for the unrenormalized SSG.
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized noises and e
In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter $beta^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the G
We study the stochastic viscous nonlinear wave equations (SvNLW) on $mathbb T^2$, forced by a fractional derivative of the space-time white noise $xi$. In particular, we consider SvNLW with the singular additive forcing $D^frac{1}{2}xi$ such that sol
Our principal focus in the present work is on one-dimensional kink-antikink and two-dimensional kink-antikink stripe interactions in the sine-Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an anti
In this paper, we study the long-time dynamics and stability properties of the sine-Gordon equation $$f_{tt}-f_{xx}+sin f=0.$$ Firstly, we use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the sol