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Global regularity for the nonlinear wave equation with slightly supercritical power

Maria Colombo and Silja Haffter

Vol. 16 (2023), No. 3, 613–642
Abstract

We consider the defocusing nonlinear wave equation u = |u|p1u in 3 × [0,). We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p = 5 + δ, where δ (0,δ0(M0)).

Keywords
nonlinear wave equation, global regularity, supercritical equation
Mathematical Subject Classification 2010
Primary: 35B65, 35L15, 35L70
Milestones
Received: 3 December 2019
Revised: 30 July 2021
Accepted: 6 October 2021
Published: 25 May 2023
Authors
Maria Colombo
EPFL
School of Basic Sciences
Lausanne
Switzerland
Institute for Advanced Study
Princeton, NJ
United States
Silja Haffter
EPFL
School of Basic Sciences
Lausanne
Switzerland

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