Infoscience

Journal article

# A class of large global solutions for the wave-map equationchi

In this paper we consider the equation for equivariant wave maps from $\R^{3+1}$ to $\Sf^3$ and we prove global in forward time existence of certain $C^\infty$-smooth solutions which have infinite critical Sobolev norm $\dot{H}^{\frac{3}{2}}(\R^3)\times \dot{H}^{\frac{1}{2}}(\R^3)$. Our construction provides solutions which can moreover satisfy the additional size condition $\|u(0, \cdot)\|_{L^\infty(|x|\geq 1)}>M$ for arbitrarily chosen $M>0$. These solutions are also stable under suitable perturbations. Our method, strongly inspired by \cite{krsc}, is based on a perturbative approach around suitably constructed approximate self--similar solutions.

#### Reference

• EPFL-ARTICLE-207512

Record created on 2015-04-21, modified on 2017-05-12