Markov processes and magneto-hydrodynamics equations. (English. Russian original) Zbl 1474.60172

J. Math. Sci., New York 258, No. 6, 739-757 (2021); translation from Zap. Nauchn. Semin. POMI 486, 7-34 (2019).
Summary: 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.


60H30 Applications of stochastic analysis (to PDEs, etc.)
60J25 Continuous-time Markov processes on general state spaces
76W05 Magnetohydrodynamics and electrohydrodynamics
78A25 Electromagnetic theory (general)
Full Text: DOI


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