We derive a probabilistic interpretation of a generalized solution of the Cauchy problem for a three-dimensional system of magneto-hydrodynamics equations called the MHD-Burgers system. First we regularize the system under consideration and prove that there exists a unique measurevalued solution of the Cauchy problem for the regularized system. Next we justify a limiting procedure with respect to the regularization parameter and, as a consequence, prove the existence and uniqueness of a solution to the Cauchy problem of the original MHD-Burgers system. Finally, we derive a probabilistic representation of the Cauchy problem solution for the MHD-Burgers system.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 7–34.
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Belopolskaya, Y.I. Markov Processes and Magneto-Hydrodynamics Equations. J Math Sci 258, 739–757 (2021). https://doi.org/10.1007/s10958-021-05577-y