Global well-posedness for the radial defocusing cubic wave equation on R3 and for rough data
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Date
2007-11-30
Authors
Roy, Tristan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Nonlinear Schrödinger equation, Well-posedness
Citation
Roy, T. (2007). Global well-posedness for the radial defocusing cubic wave equation on R3 and for rough data. <i>Electronic Journal of Differential Equations, 2007</i>(166), pp. 1-22.
Rights
Attribution 4.0 International