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On a class of solutions to the generalized KdV type equation (1802.07345v1)

Published 20 Feb 2018 in math.AP

Abstract: We consider the IVP associated to the generalized KdV equation with low degree of non-linearity \begin{equation*} \partial_t u + \partial_x3 u \pm |u|{\alpha}\partial_x u = 0,\; x,t \in \mathbb{R},\;\alpha \in (0,1). \end{equation*} By using an argument similar to that introduced by Cazenave and Naumkin [2] we establish the local well-posedness for a class of data in an appropriate weighted Sobolev space. Also, we show that the solutions obtained satisfy the propagation of regularity principle proven in [3] in solutions of the $k$-generalized KdV equation.

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