We show that a certain stochastic perturbation of the flow perfect incompressible fluid under some special external force on flat n-dimensional torus yields solution Navier–Stokes equation without in tangent space at unit volume preserving diffeomorphism group. If is absent, turns into one Reynolds type. For diffuse matter this construction Burgers equation.

We derive a probabilistic interpretation of generalized solution the Cauchy problem for three-dimensional system magneto-hydrodynamics equations called MHD-Burgers system. First we regularize under consideration and prove that there exists unique measurevalued regularized Next justify limiting procedure with respect to regularization parameter and, as consequence, existence uniqueness original ...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...