A generalization of the weighted Strichartz estimates for wave equations and an application to self-similar solutions

DOI10.1002/cpa.20133zbMath1109.35021OpenAlexW2036652100MaRDI QIDQ3418094

Jun Kato, Tohru Ozawa, Makoto Nakamura

Publication date: 2 February 2007

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2115/17152

zbMATH Keywords

wave equationself-similar solutionsCauchy problemnonlinear wave equationsweighted Strichartz estimatesexpansion by spherical harmonics

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (9)

Self-similar solutions of semilinear wave equation with variable speed of propagation ⋮ SOBOLEV INEQUALITIES WITH SYMMETRY ⋮ Anomalous solutions to nonlinear hyperbolic equations ⋮ Global existence for the one-dimensional second order semilinear hyperbolic equations ⋮ On Hartree equations with derivatives ⋮ Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type ⋮ Small data global well‐posedness for the nonlinear wave equation with nonlocal nonlinearity ⋮ On self-similar solutions of semilinear wave equations in higher space dimensions ⋮ Weighted Strichartz estimates with angular regularity and their applications

Cites Work

• Theory of function spaces II
• Blow-up for semilinear wave equations with slowly decaying data in high dimensions

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