Dissipative solutions and Markov selection to the complete stochastic Euler system

Thamsanqa Castern Moyo

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Abstract

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 exist in the sense distributions). In particular, we show that existence and weak-strong principle (i.e. a weak measure-valued solution coincides with a strong solution provided the later exists) hold true provided they satisfy some form of energy balance. Finally, we show the existence of Markov selection to the associated martingale problem.
Original languageEnglish
Pages (from-to)408-464
Number of pages57
JournalJournal of Differential Equations
Volume365
Early online date28 Apr 2023
DOIs
Publication statusPublished - 25 Aug 2023

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