Abstract
We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.
Supported partly by the Wittgenstein 2000 Award of Peter Markowich, funded by the Austrian Science Foundation (FWF), research grants of DFG (436 RUS 113/615/0-1(R)) and RFBR (01-0104002).
On leave Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia. Supported partly by Max Planck Institute for the Mathematics in Sciences (Leipzig) and the Austrian Science Foundation (FWF) START Project (Y-137-TEC) of Norbert Mauser.
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© 2004 Springer-Verlag Wien
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Imaikin, V., Komech, A., Spohn, H. (2004). Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit. In: Jüngel, A., Manasevich, R., Markowich, P.A., Shahgholian, H. (eds) Nonlinear Differential Equation Models. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0609-9_11
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DOI: https://doi.org/10.1007/978-3-7091-0609-9_11
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