Stochastic flows with stationary distribution for two-dimensional inviscid fluids

Sergio Albeverio and Raphael Høegh-Krohn

Stochastic Processes and their Applications, 1989, vol. 31, issue 1, 1-31

Abstract: We consider the Euler equation for an incompressible fluid in a general bounded domain of 2 with stochastic initial data. Extending previous work (for a fluid in a periodic box) we prove that the distribution of velocities u given as the standard normal distribution [mu][beta][gamma] with respect to the quadratic form [gamma]S(u) + [beta]H(u), with [beta], [gamma] >= 0, S, H being respectively the entropy and energy, is infinitesimally invariant with respect to the dynamics given by the Euler equation, in the sense that there is a one parameter group of unitary operators in L2([mu][beta][gamma]) with generator coinciding on a dense domain with the Liouville operator associated to the Euler flow. We also mention problems connected with proving the global invariance and the uniqueness of the stochastic flow.

Keywords: Euler; equation; stochastic; flow; incompressible; fluid; stochastic; initial; data (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (2)

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