Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet

TL;DR

This paper proves the existence of unique local solutions for a stochastic geometric wave equation driven by fractional Brownian noise, even with very rough initial data, on a one-dimensional Minkowski space.

Contribution

It establishes the existence and uniqueness of solutions under low regularity conditions, extending the understanding of stochastic wave equations with fractional noise.

Findings

Existence of unique local solutions for the stochastic geometric wave equation.

Solutions are valid even with initial data below energy critical regularity.

The approach handles fractional Brownian sheet-driven noise.

Abstract

We announce a result on the existence of a unique local solution to a stochastic geometric wave equation on the one dimensional Minkowski space $\mathbb{R}^{1+1}$ with values in an arbitrary compact Riemannian manifold. We consider a rough initial data in the sense that its regularity is lower than the energy critical.