Fifteen years ago, I wrote a paper entitled Global regularity of wave maps. II. Small energy in two dimensions, in which I established global regularity of wave maps from two spatial dimensions to the unit sphere, assuming that the initial data had small energy. 1,143 more words

## Tags » Math.AP

#### Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation

I’ve just posted to the arXiv my paper “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation“. This paper is loosely in the spirit of… 1,210 more words

#### Notes on the Nash embedding theorem

Throughout this post we shall always work in the smooth category, thus all manifolds, maps, coordinate charts, and functions are assumed to be smooth unless explicitly stated otherwise. 2,833 more words