2004/04/30 by S V Lototskii, С В Лотоцкий, B. L. Rozovskiĭ +1 · 1 citation
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Stochastic processes and financial applications
paper · doi:10.1070/rm2004v059n02abeh000719
crossref issued 2004/04/30 · crossref published 2004/04/30 · crossref published-print 2004/04/30 · openalex publication_date 2004/04/30 · crossref created 2004/07/15 · crossref published-online 2007/10/17 · crossref deposited 2025/05/12 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31
The time evolution of a passive scalar in a turbulent homogeneous incompressible Gaussian flow is considered. The turbulent nature of the flow results in non-smooth coefficients of the corresponding evolution equation. A strong solution (in the probabilistic sense) of the equation is constructed by using the Wiener Chaos expansion, and properties of the solution are studied. In particular, a certain -regularity of the solution and a representation formula of Feynman-Kac type (or a Lagrangian formula) are among the results obtained. The results can be applied to both viscous and conservative flows.