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Diffusion Approximation for Self-Similarity of Stochastic Advection in Burgers’ Equation

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Abstract

Self-similarity of Burgers’ equation with stochastic advection is studied. In self-similar variables a stationary solution is constructed which establishes the existence of a stochastically self-similar solution for the stochastic Burgers’ equation. The analysis assumes that the stochastic coefficient of advection is transformed to a white noise in the self-similar variables. Furthermore, by a diffusion approximation, the long time convergence to the self-similar solution is proved in the sense of distribution.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, China

    Wei Wang

  2. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, Australia

    A. J. Roberts

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  1. Wei Wang
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  2. A. J. Roberts
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Correspondence to Wei Wang.

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Communicated by L. Caffarelli

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Wang, W., Roberts, A.J. Diffusion Approximation for Self-Similarity of Stochastic Advection in Burgers’ Equation. Commun. Math. Phys. 333, 1287–1316 (2015). https://doi.org/10.1007/s00220-014-2117-7

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  • DOI: https://doi.org/10.1007/s00220-014-2117-7

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