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Uniform boundedness of the magnetic field in a resistive plasma

While the magnetic energy in a plasma can be easily bounded by classical energy inequalities, the behaviour of the maximum of the magnetic field is less clear. In fact, the field in chaotic flows appears to concentrate in progressively smaller regions of the domain, so that conceivably it could grow there without limit. However, we prove that as long as the magnetic energy and the plasma remain bounded, so does the magnetic field. The dependence of these bounds on the main plasma parameters is analysed. Copyright © 2003 John Wiley & Sons, Ltd.