An integrodifferential equation driven by fractional Brownian motion

TL;DR

This paper establishes the well-posedness of an integrodifferential equation modeling vortex filaments in turbulent fluids, driven by fractional Brownian motion with Hurst parameter greater than 1/2, proving global existence and uniqueness.

Contribution

It introduces a novel analysis of an integrodifferential equation driven by fractional Brownian motion, demonstrating global solutions in Sobolev spaces.

Findings

Proves global existence of solutions.

Establishes uniqueness of solutions.

Analyzes equations driven by fractional Brownian motion.

Abstract

This paper deals with the well posedness of an integrodifferential equation that describes a vortex filament associated to a 3D turbulent fluid flow. This equation is driven by a fractional Brownian motion of Hurst parameter H>1/2. We prove global existence and uniqueness of solutions in a functional space of Sobolev type.