Viscosity Limit of Stationary Distributions for the Random Forced Burgers Equation

  title={Viscosity Limit of Stationary Distributions for the Random Forced Burgers Equation},
  author={Diogo A. Gomes and Renato Iturriaga and Konstantin Khanin and Pablo Padilla},
  journal={Moscow Mathematical Journal},
We prove convergence of stationary distributions for the randomly forced Burgers and Hamilton–Jacobi equations in the limit when viscosity tends to zero. It turns out that for all values of the viscosity ν there exists a unique (up to an additive constant) global stationary solution to the randomly forced Hamilton–Jacobi equation. The main result follows from the convergence of these solutions in a limit when ν tends to zero without changing its sign. The two limiting solutions (for different… 
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