Geodesic
Markov processes and magneto-hydrodynamic systems
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 7-34

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We derive a stochastic interpretation of a generalised solution of the Cauchy problem for a 3-dimensional magneto-hydrodynamic system, called MHD-Burgerssystem. We construct a mollified MHD-Burgers system and prove the the existence and uniqueness of a measure-valued solution of the Cauchy problem for this system. Finally, we justify a limiting procedure with respect to a mollification parameter and thus prove existence and uniqueness of the Cauchy problem solution for the original MHD-Burgers system. We construct as well a probabilistic representation of this solution. 
@article{ZNSL_2019_486_a0,
     author = {Ya. I. Belopolskaya},
     title = {Markov processes and magneto-hydrodynamic systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--34},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a0/}
}
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Ya. I. Belopolskaya. Markov processes and magneto-hydrodynamic systems. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 7-34. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a0/