The critical nonlinear wave equation in two space dimensions

DOI10.4171/JEMS/404zbMath1282.35245OpenAlexW1982911890MaRDI QIDQ363234

Michael Struwe

Publication date: 2 September 2013

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/404

zbMATH Keywords

well-posednesscritical nonlinearityMoser-Trudinger estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)

Related Items (13)

Blow-up analysis for two kinds of nonlinear wave equations ⋮ Scattering for a critical nonlinear wave equation in two space dimensions ⋮ On the existence time of local solutions for critical semilinear Schrödinger equations in Sobolev spaces ⋮ A note on strong instability of standing waves for some semilinear wave and heat equations ⋮ A note on the instability of a focusing nonlinear damped wave equation ⋮ Unnamed Item ⋮ A blowing up wave equation with exponential type nonlinearity and arbitrary positive energy ⋮ Fourth-order damped wave equation with exponential growth nonlinearity ⋮ Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity ⋮ Scattering in the weighted \( L^2 \)-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity ⋮ On nonlinear Schrödinger equations derived from the nonrelativistic limit of nonlinear Klein-Gordon equations in de Sitter spacetime ⋮ Remarks on the Cauchy problem of Klein-Gordon equations with weighted nonlinear terms ⋮ A note on global well-posedness and blow-up of some semilinear evolution equations

Cites Work

• Scattering for the two-dimensional energy-critical wave equation
• Strichartz type estimates and the well-posedness of an energy critical 2D wave equation in a bounded domain
• Global well-posedness of the Cauchy problem for a super-critical nonlinear wave equation in two space dimensions
• Well- and ill-posedness issues for energy supercritical waves
• Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity
• GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL DEFOCUSING NONLINEAR WAVE EQUATION FOR SPHERICALLY SYMMETRIC DATA
• On uniqueness and stability for supercritical nonlinear wave and Schrodinger equations
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