| Abstract: |
| We discuss the generalized Korteweg de Vries (KdV) equation with nonlinear term of order three: $\partial_x(u^{3+1})$. We prove sharp local well--posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well--posedness theory of the generalized KdV which remained open after the seminal work of [Colliander--Kenig, 2002]. The existence is shown via contraction argument centered about the linear solution. The estimates necessary to close the contraction are obtained by leveraging a nonlinear smoothing effect. |
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