Probabilistic well-posedness for the nonlinear wave equation on $B_2\times\mathbb{T}$

TL;DR

This paper proves that the subcubic nonlinear wave equation on a specific domain is well-posed with high probability when initial data is randomly chosen with radial symmetry, expanding understanding of wave behavior under randomness.

Contribution

It introduces probabilistic well-posedness results for the nonlinear wave equation on a bounded domain with radial symmetry and boundary conditions, a novel setting for such analysis.

Findings

Probabilistic well-posedness established for the nonlinear wave equation.

Initial data with radial symmetry leads to well-posedness results.

Results apply to the domain $B_2\times\mathbb{T}$ with Dirichlet boundary conditions.

Abstract

We establish probabilistic well-posedness results for the subcubic nonlinear wave equation, posed on the domain $B_2\times\mathbb{T}$, with randomly chosen initial data having radial symmetry in the $B_2$ variable, and with vanishing Dirichlet boundary conditions on $\partial B_2\times\mathbb{T}$.