Markovian solutions of inviscid Burgers equation

Details Markovian solutions of inviscid Burgers equation Markovian solutions of inviscid Burgers equation

2003-02-10

arxiv.org/abs/nlin/0302016v1

Nonlinear Sciences

Chaotic Dynamics

8 pages

Scientific paper

10.1023/B:JOSS.0000003120.32992.

For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller-Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg-Martin's (white noise initial velocity) and Carraro-Duchon's L\'evy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases.

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