Can I read Three-dimensional Stochastic Cubic Nonlinear Wave Equation with Almost Space-time White Noise on EtoBox?

Three-dimensional Stochastic Cubic Nonlinear Wave Equation with Almost Space-time White Noise by Oh, Tadahiro; Wang, Yuzhao; Zine, Younes is a scholarly article available to read on EtoBox.

What is Three-dimensional Stochastic Cubic Nonlinear Wave Equation with Almost Space-time White Noise about?

We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus $\mathbb{T}^3$. In particular, we prove local well-posedness of the (renormalized) SNLW when the noise is almost a space-time white noise. In recent years, the paracontrolled calculus has played a crucial role in the well-posedness study of singular SNLW on $\mathbb{T}^3$ by Gubinelli, Koch, and the first author (2018), Okamoto, Tolomeo, and the first author (2020), and Bringmann (2020). Our approach, however, does not rely on the paracontrolled calculus. We instead proceed with the second order expansion and study the resulting equation for the residual term, using multilinear dispersive smoothing.

Author

Oh, Tadahiro; Wang, Yuzhao; Zine, Younes

Published

2021

Language

EN