On Weak-Strong Uniqueness for Stochastic Equations of Incompressible Fluid Flow

We introduce a concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing motion an inviscid incompressible fluid. These solutions are characterized by parametrized Young measure and concentration defect in total energy balance. Moreover, they weak probabilistic sense i.e., underlying probability space driving Wiener process intrinsic parts solution. first exhibit relative inequality for driven multiplicative noise then demonstrate pathwise weak-strong uniqueness principle. Finally, we also provide sufficient condition, á la Prodi (Ann Mat Pura Appl 48:173–182, 1959) Serrin (in: Nonlinear problems, University Wisconsin Press, Madison, Wisconsin, pp 69–98, 1963), Navier–Stokes system class finite solutions.