Well-posedness for the heat flow of polyharmonic maps with rough initial data

TL;DR

This paper proves local and global well-posedness for the heat flow of polyharmonic maps from Euclidean space to compact manifolds, even with rough initial data characterized by small BMO norms.

Contribution

It establishes well-posedness results for polyharmonic map heat flow with initial data having small BMO norms, extending previous work to rough initial conditions.

Findings

Proves local well-posedness for rough initial data.

Establishes global well-posedness under small BMO norm conditions.

Demonstrates stability of solutions with respect to initial data.

Abstract

We establish both local and global well-posedness for the heat flow of polyharmonic maps from $R^n$ to a compact Riemannian manifold without boundary for initial data with small BMO norms.