Limit theorem for the statistical solution of Burgers equation
The Cole-Hopf solutions of the one-dimensional Burgers equation of the form \[ \partial _tu+u\partial _xu=\frac {\nu}{2}\partial ^2_{xx}u,\quad x\in \mathbb R,\;t>0, \] are studied, where \(\nu >0\) is the viscosity and the initial value \(u(x,0)=-d\xi (x)/dx\) is given, in the case when the initial value is a functional of a Gaussian process. By means of the Gauss chaos decomposition limit results of the type of the ``Gaussian scenario'' are obtained with new normalization factors.
scientific article; zbMATH DE number 1554312