# Biharmonic wave maps into spheres

## TL;DR

This paper constructs global weak solutions for the biharmonic wave map equation targeting spheres, using a reformulation as a conservation law and a Ginzburg-Landau approximation, advancing understanding of high-order wave maps.

## Contribution

It introduces a novel approach to solving biharmonic wave maps into spheres via conservation law reformulation and approximation methods, providing new existence results.

## Key findings

- Established existence of global weak solutions in energy space
- Reformulated the biharmonic wave map equation as a conservation law
- Applied Ginzburg-Landau approximation to solve the equation

## Abstract

A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau type approximation.