Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview

  title={Shock Formation in Small-Data Solutions to \$3D\$ Quasilinear Wave Equations: An Overview},
  author={Gustav H. Holzegel and Sergi{\`u} Klainerman and Jared Speck and Willie Wai Yeung Wong},
  journal={arXiv: Analysis of PDEs},
In his 2007 monograph, D. Christodoulou proved a remarkable result giving a detailed descrip- tion of shock formation, for small H s -initial conditions (s sufficiently large), in solutions to the relativistic Euler equations in three space dimensions. His work provided a significant advancement over a large body of prior work concerning the long-time behavior of solutions to higher-dimensional quasilinear wave equations, initiated by F. John in the mid 1970's and continued by S. Klainerman, T… 

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