On the Division Problem for the Wave Maps Equation
Abstract
We consider Wave Maps into the sphere and give a new proof of small data global wellposedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single building block for the iteration space. Our approach to the socalled division problem is modular as it systematically uses two ingredients: atomic bilinear (adjoint) Fourier restriction estimates and an algebra property of the iteration space, both of which can be adapted to other phase functions.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.02066
 Bibcode:
 2018arXiv180702066C
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 Section 7 contains a proof of a special case of the bilinear estimate obtained in 1707.08944