Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 333, Issue 3, Pages 1287-1316Publisher
SPRINGER
DOI: 10.1007/s00220-014-2117-7
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Funding
- Australian Research Council [DP0988738]
- NSFC [11371190]
- Australian Research Council [DP0988738] Funding Source: Australian Research Council
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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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