Self-Similarity in Deterministic and Stochastic Dissipative Systems
نویسنده
چکیده
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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