Global Regularity of Wave Maps from R^{3+1} to H^2

Abstract

We consider Wave Maps with smooth compactly supported initial data of small H^{3/2}-norm from R^{3+1} to the hyperbolic plane and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb Gauge as in a recent paper by Shatah and Struwe, followed by dynamic separation as in earlier work of Klainerman and Machedon. We then rely on an adaptation of T.Tao's methods used in his recent breakthrough result on Wave Maps to spheres in low spatial dimensions.

Cited by in corpus (8)

• Energy dispersed large data wave maps in 2+1 dimensions
• The cubic Dirac equation: Small initial data in $H^{\frac{1}{2}}({\mathbb{R}}^2)$
• The cubic Dirac equation: Small initial data in $H^1({\mathbb{R}}^3)$
• On stable self-similar blow up for equivariant wave maps: The linearized problem
• Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium
• Global existence of small equivariant wave maps on rotationally symmetric manifolds
• Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map
• Optimal blowup stability for three-dimensional wave maps