Regularity of Wave-Maps in dimension 2+1

Abstract

In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps $\Phi :{\mathbb{R}}^{2+1}\to \mathcal{M}$ into general compact target manifolds $\mathcal{M}$.

31 pages

References in corpus (8)

• Energy dispersed large data wave maps in 2+1 dimensions
• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
• Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
• 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
• An inverse theorem for the bilinear $L^2$ Strichartz estimate for the wave equation
• On the Formation of Singularities in the Critical O(3) Sigma-Model
• Geometric renormalization of large energy wave maps

Cited by in corpus (54)

• Energy dispersed large data wave maps in 2+1 dimensions
• Globally regular instability of $Ad{S}_3$
• Two-bubble dynamics for threshold solutions to the wave maps equation
• Equivariant Schrödinger Maps in two spatial dimensions
• Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
• Global regularity of wave maps VII. Control of delocalised or dispersed solutions
• Soliton resolution for critical co-rotational wave maps and radial cubic wave equation
• Global regularity of wave maps III. Large energy from ${\mathbb{R}}^{1+2}$ to hyperbolic spaces
• On energy-critical half-wave maps into ${\mathbb{S}}^2$
• Universality of blow up profile for small blow up solutions to the energy critical wave map equation
• Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium
• Mode stability of self-similar wave maps in higher dimensions
• On stability of blow up solutions for the critical co-rotational Wave Maps problem
• High-frequency backreaction for the Einstein equations under polarized $\mathbb{U}(1)$ symmetry
• Overview of the proof of the Bounded $L^2$ Curvature Conjecture
• Quantization of time-like energy for wave maps into spheres
• Mathematical General Relativity
• Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem
• On the Division Problem for the Wave Maps Equation
• The hyperbolic Yang--Mills equation in the caloric gauge. Local well-posedness and control of energy dispersed solutions
• Global well-posedness for the massless cubic Dirac equation
• Global well-posedness for 2D radial Schrödinger maps into the sphere
• Threshold dynamics for corotational wave maps
• Open problems in mathematical physics
• Characterization of large energy solutions of the equivariant wave map problem: I
• An asymptotic expansion of two-bubble wave maps
• Conditional large data scattering results for the Dirac-Klein-Gordon system
• Global nonlinear stability of large dispersive solutions to the Einstein equations
• On the existence and stability of blowup for wave maps into a negatively curved target
• Global existence of small equivariant wave maps on rotationally symmetric manifolds
• Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System
• Global solutions of nonlinear wave equations with large energy
• Global wellposedness of hedgehog solutions for the (3+1) Skyrme model
• Soliton resolution along a sequence of times with dispersive error for type II singular solutions to focusing energy critical wave equation
• Global regularity of critical Schrödinger maps: subthreshold dispersed energy
• Biharmonic wave maps: Local wellposedness in high regularity
• Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map
• Energy dispersed solutions for the (4+1)-dimensional Maxwell-Klein-Gordon equation
• Long time solutions for wave maps with large data
• Optimal blowup stability for three-dimensional wave maps
• Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity
• On stable self-similar blow up for equivariant wave maps
• The energy-critical nonlinear wave equation with an inverse-square potential
• Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy
• Sharp universal rate for stable blow-up of corotational wave maps
• On blowup of co-rotational wave maps in odd space dimensions
• On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System
• Geometric solitons with vortex structures for some geometric flows from Minkowski spaces: part I
• Schrödinger Soliton from Lorentzian Manifolds
• Wave maps on (1+2)-dimensional curved spacetimes
• Non-Uniqueness of Bubbling for Wave Maps
• Scattering for the Equivariant U(1) Problem
• Global results for a Cauchy problem related to biharmonic wave maps
• The Cauchy Problem for Wave Maps on a Curved Background