Conditional Global Existence and Scattering for a Semi-Linear Skyrme Equation with Large Data

@article{Lawrie2013ConditionalGE,
  title={Conditional Global Existence and Scattering for a Semi-Linear Skyrme Equation with Large Data},
  author={Andrew Lawrie},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={334},
  pages={1025-1081}
}
  • A. Lawrie
  • Published 4 November 2013
  • Mathematics
  • Communications in Mathematical Physics
We study a generalization of energy super-critical wave maps due to Adkins and Nappi that can also be viewed as a simplified version of the Skyrme model. These are maps from 1 + 3 dimensional Minkowski space that take values in the 3-sphere, and it follows that every finite energy Adkins–Nappi wave map has a fixed topological degree which is an integer. Here we initiate the study of the large data dynamics for Adkins–Nappi wave maps by proving that there is no type II blow-up in the class of… 
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References

SHOWING 1-10 OF 37 REFERENCES
Characterization of large energy solutions of the equivariant wave map problem: I
We consider $1$-equivariant wave maps from ${\Bbb R}^{1+2}\to{\Bbb S}^2$. For wave maps of topological degree zero we prove global existence and scattering for energies below twice the energy of
Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that of the standing wave
Equivariant wave maps exterior to a ball
We consider the exterior Cauchy–Dirichlet problem for equivariant wave maps from 3 + 1 dimensional Minkowski spacetime into the three sphere. Using mixed analytical and numerical methods we show
On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces
In this paper we present a method to study global regularity properties of solutions of large-data critical Schrodinger equations on certain noncompact Riemannian manifolds. We rely on concentration
Relaxation of Wave Maps Exterior to a Ball to Harmonic Maps for All Data
In this paper we establish relaxation of an arbitrary 1-equivariant wave map from $${\mathbb{R}^{1+3}_{t,x}{\setminus} (\mathbb{R}\times B(0,1))\to S^3}$$Rt,x1+3\(R×B(0,1))→S3 of finite energy and
Asymptotic stability of the Skyrmion
We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static
On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations
Abstract We prove existence and scattering results for semilinear wave equations with low regularity data. We also determine the minimal regularity that is needed to ensure local existence and
Scattering for radial, bounded solutions of focusing supercritical wave equations
In this paper, we consider the wave equation in space dimension 3 with an energy-supercritical, focusing nonlinearity. We show that any radial solution of the equation which is bounded in the
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