Abstract
We consider the Cauchy problem of the fifth‐order Korteweg–de Vries (KdV) equations without nonlinear dispersive term Recently, Kappeler‐Molnar (2018) proved that the fifth‐order KdV equation with nonlinear dispersive term and Hamiltonian structure is globally well‐posed in with s ≥ 0. Without the nonlinear dispersive term, Equation (0.1) is not integrable, and Kappeler–Molnar's approach is not valid. Using the idea of modifying Bourgain space, we prove that Equation (0.1) is locally well‐posed in with .
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