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

TL;DR

This paper proves the well-posedness of the heat flow of biharmonic maps from Euclidean space to a compact manifold, under small initial data in BMO spaces, covering both local and global cases.

Contribution

It establishes the well-posedness results for biharmonic map heat flow with rough initial data in BMO spaces, extending previous smooth data results.

Findings

Well-posedness established for small BMO initial data

Results cover both local and global solutions

Applicable to maps into compact Riemannian manifolds

Abstract

This paper establish the local (or global, resp.) well-posedness of the heat flow of biharmonic maps from $R^n$ to a compact Riemannian manifold without boundary with small local BMO (or BMO, resp.) norms.