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- W1996603344 abstract "We consider the Cauchy problem of the fifth-order equation arising from the Korteweg-de Vries (KdV) hierarchy u_t + u_{xxxxx} + c_1u_{x} u_{xx} + c_2u u_{x} = 0 x,t in R We prove a priori bound of solutions for H^s(R) with s >= 5/4 and the local well-posedness for s >= 2. The method is a short time X^{s,b} space, which is first developed by Ionescu-Kenig-Tataru in the context of the KP-I equation. In addition, we use a weight on localized X^{s,b} structures to reduce the contribution of high-low frequency interaction where the low frequency has large modulation. As an immediate result from a conservation law, we have the fifth-order equation in the KdV hierarchy is globally well-posed in the energy space H^2." @default.
- W1996603344 created "2016-06-24" @default.
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- W1996603344 date "2012-05-03" @default.
- W1996603344 modified "2023-09-23" @default.
- W1996603344 title "Rough solutions of the fifth-order KdV equations" @default.
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- W1996603344 doi "https://doi.org/10.48550/arxiv.1205.0850" @default.
- W1996603344 hasPublicationYear "2012" @default.
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