Unbounded rough drivers, rough PDEs and applications

TL;DR

This paper reviews recent advances in rough partial differential equations using the unbounded rough driver framework, highlighting applications to models like Landau-Lifshitz-Gilbert, Navier-Stokes, and Euler equations.

Contribution

It introduces the unbounded rough driver formalism and demonstrates its application to several important PDE models, advancing the theoretical understanding.

Findings

Unified framework for rough PDEs using unbounded rough drivers

Application to classical fluid and magnetization models

Enhanced understanding of rough PDE solution behavior

Abstract

A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present applications to concrete models including Landau-Lifshitz-Gilbert, Navier-Stokes and Euler equations.