Relaxation of wave maps exterior to a ball to harmonic maps for all data.(English)Zbl 1288.35356

Summary: We establish relaxation of an arbitrary 1-equivariant wave map from $$\mathbb R^{1+3}_{t,x}\setminus (\mathbb R\times B(0,1))\to S^3$$ of finite energy and with a Dirichlet condition at $$r=1$$, to the unique stationary harmonic map in its degree class. This settles a recent conjecture of Bizoń, Chmaj, Maliborski who observed this asymptotic behavior numerically.

MSC:

 35L71 Second-order semilinear hyperbolic equations 35C08 Soliton solutions 35L20 Initial-boundary value problems for second-order hyperbolic equations
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