Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class

Abstract

Using the harmonic map heat flow and the function spaces of Tataru and the author, we establish a large data local well-posedness result in the energy class for wave maps from two-dimensional Minkowski space ${\mathbb{R}}^{1+2}$ to hyperbolic spaces $\H^m$. This is one of the five claims required in an earlier paper in this series to prove global regularity for such wave maps.

73 pages, no figures. Will not be published in current form, pending future reorganisation of the heatwave project

References in corpus (5)

• Global regularity of wave maps II. Small energy in two dimensions
• Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
• Global regularity of wave maps VII. Control of delocalised or dispersed solutions
• Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions
• Global behaviour of nonlinear dispersive and wave equations

Cited by in corpus (13)

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• Geometric renormalization below the ground state
• On stability of blow up solutions for the critical co-rotational Wave Maps problem
• Quantization of time-like energy for wave maps into spheres
• The hyperbolic Yang--Mills equation in the caloric gauge. Local well-posedness and control of energy dispersed solutions
• Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in $H^1$
• Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case
• Convergence to harmonic maps for the Landau-Lifshitz flows on two dimensional hyperbolic spaces
• Long time solutions for wave maps with large data
• Bilinear Strichartz estimates for the Schr{ö}dinger map problem
• On the stability of certain spin models in 2+1 dimensions
• The Cauchy Problem for Wave Maps on a Curved Background