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In this paper we prove that the fifth order equation arising from the KdVhierarchy $ \partial_tu + \partial_x^5u + c_1\partial_x u\partial_x^2u +c_2u\partial_x^3u = 0 $ is locally well-posed in $ H^s(\mathbb{R}) $ for $ s>5/2. Also, we prove the solution map of the equation is not uniformlycontinuous for $s>0$.

On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map