Stochastic flows with stationary distribution for two-dimensional inviscid fluids
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.
Year of publication: |
1989
|
---|---|
Authors: | Albeverio, Sergio ; Høegh-Krohn, Raphael |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 31.1989, 1, p. 1-31
|
Publisher: |
Elsevier |
Keywords: | Euler equation stochastic flow incompressible fluid stochastic initial data |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Schrödinger operators with point interactions and short range expansions
Albeverio, Sergio, (1984)
-
A random walk on p-adics--the generator and its spectrum
Albeverio, Sergio, (1994)
-
Albeverio, Sergio, (1997)
- More ...