Abstract. We show local existence of solutions to a two-component Hunter– Saxton system. Moreover, we prove that the slopes of solutions can become unbounded. Finally, if initial data satisfy appropriate smallness conditions, the associated flow is global. 1. Introduction. We introduce the two-component Hunter–Saxton system of equations utxx + 2 ux uxx + u uxxx − κρ ρx = 0, t> 0, x ∈ R ⎪ ⎨ u(t, x + 1) = u(t, x), t ≥ 0, x ∈
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