Electron. J. Diff. Eqns., Vol. 2007(2007), No. 166, pp. 1-22.

Global well-posedness for the radial defocusing cubic wave equation on R3 and for rough data

Tristan Roy

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

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Tristan Roy
UCLA Mathematics Department, Box 951555
Los Angeles, CA 90095-1555, USA
email: triroy@math.ucla.edu

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