an:01639857
Zbl 0984.60078
Bertoin, Jean
Some properties of Burgers turbulence with white or stable noise initial data
EN
Barndorff-Nielsen, Ole E. (ed.) et al., L??vy processes. Theory and applications. Boston: Birkh??user. 267-279 (2001).
2001
a
60H30 35Q53
Burgers equation; white noise; stable process
The author reviews some qualitative and quantitative results on the weak solution to the inviscid Burgers equation \(\partial_t u+\partial(u^2/2)=0\) with random initial datum. (The solution is defined as the limit \(u_0=\lim_{\varepsilon\downarrow 0}u_\varepsilon\), where \(u_\varepsilon\) is a unique solution of the Burgers equation \(\partial_t u+\partial(u^2/2)=\varepsilon\partial^2_{xx}u\).) Specifically, he first considers the case where the initial datum is a white noise (the derivative in the Schwartz sense of a two-sided Brownian motion). Then he discusses some extensions to a stable noise (the derivative in the Schwartz sense of a stable L??vy process with index \(\alpha\in(1/2,2]\)).
For the entire collection see [Zbl 0961.00012].
Vigirdas Mackevi??ius (Vilnius)