Bubbling location for F-harmonic maps and Inhomogeneous Landau-Lifshitz equations

2005/04/25 by Yuxiang Li, Li, Yuxiang, Youde Wang +1
Mathematics · Physics and Astronomy · #35Q60 #58E20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35Q60 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0504502

13pages

arxiv created 2005/08/08 · arxiv updated 2009/12/01

Abstract

Let f be a positive smooth function on a close Riemann surface (M,g). The f-energy of a map u from M to a Riemannian manifold (N,h) is defined as E_f(u)=∫_Mf|∇ u|²dV_g. In this paper, we will study the blow-up properties of Palais-Smale sequences for E_f. We will show that, if a Palais-Smale sequence is not compact, then it must blows up at some critical points of f. As a sequence, if an inhomogeneous Landau-Lifshitz system, i.e. a solution of u_t=u×τ_f(u)+τ_f(u),\s u:M→ S² blows up at time ∞, then the blow-up points must be the critical points of f.

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