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Local well-posedness of the fifth-order KdV-type equations on the half-line. (English) Zbl 1484.35333

A fifth order dispersive equation of Korteweg-de Vries type \[\partial_tu-\partial_x^5u+F(u)=0\] is studied on the half-line \(x\in\mathbb R^+\). A couple of local well-posedness results for nonlinearities motivated by hydrodynamic applications is proved using delicate multilinear estimates.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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