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Self-similarity in deterministic and stochastic dissipative systems

Jack Xin

Analysis of PDEs mathscidoc:1912.43922

BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA, 31, (2), 75-94, 2003.6
In this paper, self-similarity is illustrated and compared in deterministic and stochastic dissipative systems. Examples are (1) deterministic self-similarity in reaction-diffusion system and Navier-Stokes equations, where solutions eventually decay to zero due to balance of diffusion (viscosity) and nonlinearity;(2) statistical self-similarity in randomly advected passive scalar model of Kraichnan where solutions undergo turbulent decay due to roughness of advection;(3) selfsimilarity in blowup of solutions of fourth order nonlinear parabolic equations of the Cahn-Hillard type. Problems for future research are mentioned, especially those where self-similarity is conjectured based on numerical evidence or physical grounds but mathematically open.
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@inproceedings{jack2003self-similarity,
  title={Self-similarity in deterministic and stochastic dissipative systems},
  author={Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210652904325486},
  booktitle={BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA},
  volume={31},
  number={2},
  pages={75-94},
  year={2003},
}
Jack Xin. Self-similarity in deterministic and stochastic dissipative systems. 2003. Vol. 31. In BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA. pp.75-94. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210652904325486.
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