What is it about?
In fluid dynamics governed by the one dimensional inviscid Burgers equation $\partial_t u+u\partial_x u=0$, the stirring is explained by the sticky particles model. A Markov process $([Z^1_t,Z^2_t],\,t\geq0)$ describes the motion of random turbulent intervals which evolve inside an other Markov process $([Z^3_t,Z^4_t],\,t\geq0)$, describing the motion of random clusters concerned with the turbulence. Then, the four velocity processes $(u(Z^i_t,t),\,t\geq0)$ are backward semi-martingales. If one of them is a martingale, then any turbulent interval is reduced to a single point.
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Why is it important?
We look at Burgers' turbulence from a new angle, through stochastic processes (semi-martingales.) Which define random intervals that we have called "turbulent intervals". We define a random variable which models the shocks and which allows us to look at the detection of the first instants of turbulence.
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This page is a summary of: Backward semi-martingales into Burgers turbulence, Journal of Mathematical Physics, June 2021, American Institute of Physics, DOI: 10.1063/5.0036721.
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