Geodesic
Central limit theorem for Burgers equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 7-13

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Suppose the potential of the initial field of the Cauchy problem for the Burgers equation is a homogeneous mean-square continuous Gaussian random field. We show that the correlation function of this field is summable absolutely or its square is summable. Then in the limit $t\to\infty$ the field of solutions of the original equation tends in its distribution to a Gaussian random vector field. 
@article{TMF_1991_88_1_a1,
     author = {O. O. Griniv},
     title = {Central limit theorem for {Burgers} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {7--13},
     publisher = {mathdoc},
     volume = {88},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a1/}
}
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O. O. Griniv. Central limit theorem for Burgers equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 7-13. http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a1/