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