# 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} }

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…

## 6 Citations

Conditional Stable Soliton Resolution for a Semi-linear Skyrme Equation

- MathematicsAnnals of PDE
- 2019

We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from $(1+3)$-dimensional Minkowski space into the $3$-sphere and 1-forms on…

Profile decompositions for wave equations on hyperbolic space with applications

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- 2014

The goal for this paper is twofold. Our first main objective is to develop Bahouri–Gérard type profile decompositions for waves on hyperbolic space. Recently, such profile decompositions have proved…

Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm

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- 2014

In this paper we study the focusing cubic wave equation in 1 + 5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target…

Long-time dynamics for the energy-critical harmonic map heat flow and nonlinear heat equation

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- 2017

The main focus of this thesis is on critical parabolic problems, in particular, the harmonic map heat flow into the 2-sphere ~ut = ∆~u+ |∇~u|~u, ~u : R → S, and the focusing nonlinear heat equation…

Linear stability of the Skyrmion

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- 2016

We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.

Decay for Skyrme wave maps

- Mathematics, Physics
- 2021

We consider the decay problem for global solutions of the Skyrme and AdkinsNappi equations. We prove that the energy associated to any bounded energy solution of the Skyrme (or Adkins-Nappi) equation…

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