Summary
Non-linear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with «unconditional» stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem.
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Tasso, H. Remarks on non-linear stability in dissipative magnetohydrodynamics. Il Nuovo Cimento B 108, 827–830 (1993). https://doi.org/10.1007/BF02741882
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DOI: https://doi.org/10.1007/BF02741882