Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$

Details Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$ Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$

2007-10-05

arxiv.org/abs/0710.1115v2

Mathematics

Analysis of PDEs

16 pages. Error in the first version of this paper "Global well-posedness for solutions of low regularity to the defocusing cu

Scientific paper

We prove global well-posedness for the defocusing cubic wave equation with data in $H^{s} \times H^{s-1}$, $1>s>{13/18}$. 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.

Affiliated with

Also associated with

No associations

Rating

Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On $\mathbb{R}^{3}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-328514