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Abstract:
In a previous note [Tasso, Phys. Plasmas 2, 1789 (1995)], dissipative magnetized Trkal flows were proved to be Lyapunov stable nonlinearly under the conditions of sufficiently small Reynolds number and of an upper bound of the "force-free" current. An alternative Lyapunov functional containing the cross helicity and introduced recently for conservative magnetized Beltrami flows [Yoshida et al., J. Math. Phys. 44, 2168 (2003)] is extended here to the Trkal flows mentioned above. Stability is now proven under limitations on maximal velocity and current without introducing an upper bound on the Reynolds number.
