Small-data shock formation in solutions to 3D quasilinear wave equations: an overview. (English) Zbl 1346.35005
The goal of this paper is to present an overview of D. Christodoulou’s results [The formation of shocks in 3-dimensional fluids. Zürich: EMS Publishing House (2007; Zbl 1117.35001)] on shock formations and their more recent extensions for two important classes of quasilinear 3D wave equations.
Reviewer: Evgeniy Panov (Novgorod)
MSC:
| 35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 58J45 | Hyperbolic equations on manifolds |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 35Q31 | Euler equations |
| 35L72 | Second-order quasilinear hyperbolic equations |
Keywords:
characteristic hypersurfaces; eikonal function; generalized energy estimates; null condition; vectorfield method; Raychaudhuri equation; Riccati equationCitations:
Zbl 1117.35001References:
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