Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field
نویسندگان
چکیده
Time evolution of a passive scalar is considered in a turbulent homogeneous incompressible Gaussian flow. The turbulent nature of the flow results in non-smooth coefficients in the corresponding evolution equation. A strong, in the probabilistic sense, solution of the equation is constructed using Wiener Chaos expansion, and the properties of the solution are studied. Among the results obtained are a certain Lp-regularity of the solution and Feynman-Kac-type, or Lagrangian, representation formula. The results apply to both viscous and conservative flows. Published in Russian Mathematical Surveys (Russ. Math. Surv.), 2004, 59 (2), 297-312.
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August 20, 2003 TIME EVOLUTION OF A PASSIVE SCALAR IN A TURBULENT INCOMPRESSIBLE GAUSSIAN VELOCITY FIELD
Passive scalar equation is considered in a turbulent homogeneous incompressible Gaussian velocity field. The turbulent nature of the field results in non-smooth coefficients in the equation. A strong, in the stochastic sense, solution of the equation is constructed using the Wiener Chaos, and the properties of the solution are studied. The results apply to both viscous and conservative motions....
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