2015/06/18 by Kazuo Kobayasi, Kobayasi, Kazuo, Dai Noboriguchi +1
Economics, Econometrics and Finance · Engineering · Mathematics · #35L04 #60H15 #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1506.05758
openalex publication_date 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation one obtains a result of uniqueness and existence. The unique solution is the limit of the solution of the stochastic parabolic approximation.