Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 166, pp. 1-22.

Title: Global well-posedness for the radial defocusing cubic wave equation
       on R^3 and for rough data

Author: Tristan Roy (Univ. of California, Los Angeles, CA, USA)

Abstract: 
 We prove global well-posedness for the radial defocusing cubic
 wave equation
 $$\displaylines{
 \partial_{tt} u  - \Delta u  =  -u^{3} \cr
 u(0,x) =  u_{0}(x)    \cr
 \partial_{t} u(0,x)  =  u_{1}(x)
 }$$
 with data $(u_0, u_1) \in H^{s} \times H^{s-1}$,
 $1 > s >7/10$. The proof relies upon a Morawetz-Strauss-type
 inequality that allows us to control the growth of an almost
 conserved quantity.
  
Submitted August 17, 2007. Published November 30, 2007.
Math Subject Classifications: 35Q55
Key Words: Nonlinear Schrodinger equation; well-posedness