A para-differential renormalization technique for nonlinear dispersive equations

Details A para-differential renormalization technique for nonlinear dispersive equations A para-differential renormalization technique for nonlinear dispersive equations

2009-07-27

arxiv.org/abs/0907.4649v1

Comm. Partial Differential Equations Vol. 35, No. 10, 1827-1875 (2010)

Mathematics

Analysis of PDEs

42 pages, no figures

Scientific paper

10.1080/03605302.2010.487232

For \alpha \in (1,2) we prove that the initial-value problem \partial_t
u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t;
u(0)=\phi, 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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