Vol. 5, No. 1, 2012

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A remark on barely $\dot H^{s_{p}}$-supercritical wave equations

Tristan Roy

Vol. 5 (2012), No. 1, 199–218

We prove that a good sp critical theory for the 3D wave equation ttu u = |u|p1u can be extended to prove global well-posedness of smooth solutions of at least one 3D barely sp-supercritical wave equation ttu u = |u|p1ug(|u|), with g growing slowly to infinity, provided that a Kenig-Merle type condition is satisfied. This result is related to those obtained by Tao and the author for the particular case sp = 1, showing global regularity for g growing logarithmically with radial data and for g growing doubly logarithmically with general data.

wave equation, global existence, barely supercritical
Mathematical Subject Classification 2000
Primary: 35Q55
Received: 26 April 2010
Revised: 17 July 2010
Accepted: 16 August 2010
Published: 25 June 2012

Proposed: Terence Tao
Tristan Roy
School of Mathematics
Institute for Advanced Study
Einstein Drive
Princeton, NJ 08540
Institute For Advanced Study