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

Abstract

We prove global well-posedness for the radial defocusing cubic wave equation ∂ttu - Δu = -u3 u(0, x) = u0(x) ∂tu(0, x) = u1(x) with data (u0, u1) ∈ Hs x Hs-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.