Nonconcentration of energy for a semilinear Skyrme model

Abstract

We continue our investigation of a model introduced by Adkins and Nappi, in which omega mesons stabilize chiral solitons. The aim of this article is to show that the energy associated to equivariant solutions does not concentrate.Comment: 12 pages, 2 figure

Global well-posedness and scattering for Skyrme wave maps

“…Motivated also by the profile of blow-up solutions for wave maps, we focus our attention to degree-1 equivariant maps corresponding to the two models. In this case, non-concentration of energy has been established for the 3 + 1 dimensional Adkins-Nappi model [3,4] 1 . In this article, we address the global issue.…”

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

“…for an appropriate normalizing constant c. Here ǫ is the Levi-Civita symbol, i.e., Note that (1.1) is a generalization of the Lagrangian for wave maps, where here we have now introduced a coupling between maps U : R 1+3 → S 3 and 1-forms A on R 1+3 . Following [14,16,15], we consider only a restricted class of maps U and forms A, namely we make an equivariance assumption. Let (t, r, θ, φ) be polar coordinates on R 1+3 .…”

Linear Stability of the Skyrmion

“…There is also some recent activity on the related but simpler Adkins-Nappi model, see e.g. [10,9,19]. From a numerical point of view, the linear stability of the Skyrmion is addressed in [14] and 2 [2] studies the nonlinear stability.…”