Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions

Terence Tao

Type: Article

Publication Date: 2001-12-01

Citations: 144

DOI: https://doi.org/10.1007/pl00005588

Abstract

We show that wave maps from Minkowski space ℝ1+ n to a sphere S m −1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space , in all dimensions n≥ 5. This generalizes the results in the prequel [40] of this paper, which addressed the high-dimensional case n≥ 5. In particular, in two dimensions we have global regularity whenever the energy is small, and global regularity for large data is thus reduced to demonstrating non-concentration of energy.

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