Long time dynamics for weakly damped nonlinear Klein-Gordon equations

2018/01/20 by Burq, Nicolas, Raugel, Genevieve, Schlag, Wilhelm · 1 citation
#35B40 #35BXX #35L05 #35L71 #37L10 #37L45 #37L50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.06735

Abstract

We continue our study of damped nonlinear Klein-Gordon equations. In our previous work we considered fixed positive damping and proved a form of the soliton resolution conjecture for radial solutions. In contrast, here we consider damping which decreases in time to 0. In the class of radial data we again establish soliton resolution provided the damping goes to 0 sufficiently slowly. While our previous work relied on invariant manifold theory, here we use the Lojasiewicz-Simon inequality applied to a suitable Lyapunov functional.

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• Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit

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