Table of Contents

1. Jing Wang’s Question
2. Some Suggestions

Jing Wang’s Question ↩

from jing wang wangjing699@gmail.com to “J. Colliander” colliand@math.toronto.edu date Tue, Nov 9, 2010 at 9:06 PM

Hi Jim,

Do you know some global results in the low regularity about the wave equations?

Thank you!

Best,

Jing

Some Suggestions ↩

Consider $\Box u = u^3$ in $\mathbb{R}^{1+3}$.

• I suggest you take a look at the 2003 paper of Gallagher-Planchon
• Inside that paper you will find a paper by Kenig-Ponce-Vega which proves the same result building on Bourgain’s high/low method.
• I discussed this problem in the past with Pieter Blue and Slim Ibrahim. What I recall from those conversations was that the $I$-method quickly produces the same result as obtained by the earlier works. We should look to see if any other results (maybe by Tristan Roy) have recently been obtained for this equation.