The Cauchy problem for nonlinear wave equations in the Sobolev space of critical order

DOI10.3934/dcds.1999.5.215zbMath0958.35011OpenAlexW1969354076MaRDI QIDQ1576812

Tohru Ozawa, Makoto Nakamura

Publication date: 16 August 2000

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.1999.5.215

zbMATH Keywords

initial data in supercritical Sobolev spacessmallness of the initial dataunique local in time solution

Mathematics Subject Classification ID

Related Items (10)

Well-posedness issues for some critical coupled non-linear Klein-Gordon equations ⋮ Unnamed Item ⋮ Ill-posedness of \(H^1\)-supercritical waves ⋮ Scattering for the two-dimensional energy-critical wave equation ⋮ On the lack of compactness in the 2D critical Sobolev embedding ⋮ Sharp energy criteria of blow-up for the energy-critical Klein-Gordon equation ⋮ Strichartz type estimates and the well-posedness of an energy critical 2D wave equation in a bounded domain ⋮ Scattering below the ground state for the 2D non-linear Schrödinger and Klein–Gordon equations revisited ⋮ On existence and uniqueness of solutions for semilinear fractional wave equations ⋮ Double logarithmic inequality with a sharp constant

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