Small-data shock formation in solutions to 3D quasilinear wave equations: An overview

DOI10.1142/S0219891616500016zbMath1346.35005arXiv1407.6276OpenAlexW3099658961MaRDI QIDQ2798337

Gustav Holzegel, Jared Speck, Sergiu Klainerman, Willie Wai Yeung Wong

Publication date: 12 April 2016

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6276

zbMATH Keywords

Riccati equationgeneralized energy estimatesnull conditionRaychaudhuri equationcharacteristic hypersurfaceseikonal functionvectorfield method

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Hyperbolic conservation laws (35L65) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Hyperbolic equations on manifolds (58J45) Euler equations (35Q31) Second-order quasilinear hyperbolic equations (35L72)

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Cites Work

• The bounded \(L^2\) curvature conjecture
• The formation of black holes in general relativity.
• Blowup for nonlinear hyperbolic equations
• Compressible Flow and Euler's Equations
• Delayed singularity formation in 2D compressible flow
• Almost global existence to nonlinear wave equations in three space dimensions
• Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions
• A comment on the construction of the maximal globally hyperbolic Cauchy development
• Hyperbolic Conservation Laws in Continuum Physics
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