Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$
Analysis of PDEs
2017-06-19 v2
Abstract
We prove global well-posedness for the defocusing cubic wave equation with data in , . The main task is to estimate the variation of an almost conserved quantity on an arbitrary long time interval. We divide it into subintervals. On each of these subintervals we write the solution as the sum of its linear part adapted to the subinterval and its corresponding npnlinear part. Some terms resulting from this decomposition have a controlled global variation and other terms have a slow local variation.
Keywords
Cite
@article{arxiv.0710.1115,
title = {Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$},
author = {Tristan Roy},
journal= {arXiv preprint arXiv:0710.1115},
year = {2017}
}
Comments
16 pages. Error in the first version of this paper "Global well-posedness for solutions of low regularity to the defocusing cubic wave equation on $\mathbb{R}^{3}$.". arXiv admin note: text overlap with arXiv:0708.2299