2021/12/18 by Thamsanqa Castern Moyo, Moyo, Thamsanqa Castern · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2112.09955
openalex publication_date 2021/12/18 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We introduce the concept of stochastic measure-valued solutions to the complete Euler system describing the motion of a compressible inviscid fluid subject to stochastic forcing, where the nonlinear terms are described by defect measures. These solutions are weak in the probabilistic sense (probability space is not a given `priori', but part of the solution) and analytical sense (derivatives only exists in the sense distributions). In particular, we show that: existence, weak-strong principle; a weak measure-valued solution coincides with a strong solution provided the later exists, all hold true provided they satisfy some form of energy balance. Finally, we show the existence of strong Markov selection to the associated martingale problem.