Abstract
In this paper, we study the Cauchy problem of a weakly dissipative HS equation. We first establish the local well-posedness for the weakly dissipative HS equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.
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