2010/10/01 by Anastasia Korshunova, Korshunova, Anastasia, Olga Rozanova +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35L65 #35L67 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stochastic processes and financial applications #math-ph #math.AP #math.MP #msc:35L65 #msc:35L67
paper · pdf · doi:10.48550/arxiv.1010.0212
8 pages, submitted for Proceedings of International Conference on Hyperbolic Problems, Beijing, 2010
arxiv created 2010/10/01 · openalex publication_date 2010/10/01 · arxiv updated 2010/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend our result of [1] and show that one can associate with the stochastically perturbed non-viscid Burgers equation a system of viscous balance laws. The Cauchy data for the Burgers equation generates the data for this system. Till the moment of the shock formation in the solution to the Burgers equation the above system of viscous balance laws can be reduced to the pressureless gas dynamics system (in a limit as the parameters of perturbation tend to zero). If the solution to the Burgers equation contains shocks, the limit system is equivalent to the system with a specific pressure, in some sense analogous to the pressure of barotropic monoatomic gas.