The Axisymmetric Antidynamo Theorem Revisited

نویسندگان

  • Ralf Kaiser
  • Andreas Tilgner
چکیده

The axisymmetric kinematic dynamo problem is reconsidered and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions, i.e. we assume a compressible fluid of variable (in space and time) conductivity moving in an arbitrary (axisymmetric) domain. We prove unconditional, pointwise and exponential decay of magnetic field and electric current to zero. The decay rate of the external (meridional) magnetic field can become very small (compared to free decay) for special flow fields and large magnetic Reynolds numbers. We give an example of that. On the other hand, for incompressible fluids of constant conductivity the meridional and azimuthal decay rates are always equal to those of free decay in that domain.

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عنوان ژورنال:
  • SIAM Journal of Applied Mathematics

دوره 74  شماره 

صفحات  -

تاریخ انتشار 2014