Long time solutions for wave maps with large data

Abstract

For 2 + 1 dimensional wave maps with ${\mathbb{S}}^2$ as the target, we show that for all positive numbers $T_0>0$ and $E_0>0$, there exist Cauchy initial data with energy at least $E_0$, so that the solution's life-span is at least $[0,T_0]$. We assume neither symmetry nor closeness to harmonic maps.

41 pages, 3 figures

References in corpus (11)

• Global regularity of wave maps II. Small energy in two dimensions
• Regularity of Wave-Maps in dimension 2+1
• Energy dispersed large data wave maps in 2+1 dimensions
• Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
• Global regularity of wave maps I. Small critical Sobolev norm in high dimension
• Global regularity of wave maps VII. Control of delocalised or dispersed solutions
• Global regularity of wave maps III. Large energy from ${\mathbb{R}}^{1+2}$ to hyperbolic spaces
• Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions
• Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class
• On the Global Regularity of Wave Maps in the Critical Sobolev Norm
• On the Formation of Singularities in the Critical O(3) Sigma-Model

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