A steady mixing (even Bernoulli) smooth volume-preserving vector field in a hounded container in R~3 with smooth no-slip boundary is constructed. An interesting feature is that it is structurally stable in the class of C3 volumepreserving vector fields on the given domain of R3 with smooth no-slip boundary, thus if one could think how to drive it then it would be physically realisable. It is pointed out, however, that no flow with no-slip boundaries can mix faster than 1/t~2 in time t.
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