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arXiv · 0907.4649

A para-differential renormalization technique for nonlinear dispersive equations

Sebastian Herr·Alexandru D. Ionescu·Carlos E. Kenig·Herbert Koch
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Abstract

For α\in (1,2) we prove that the initial-value problem \partial_t u+D^α\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t; u(0)=ϕ, is globally well-posed in the space of real-valued L^2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.

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Sebastian Herr, Alexandru D. Ionescu, Carlos E. Kenig, Herbert Koch. 2009-07-27. A para-differential renormalization technique for nonlinear dispersive equations. https://doi.org/10.1080/03605302.2010.487232

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