Invariant quantities of the classical motion of an ideal incompressible fluid in a two-dimensional bounded domain are used to construct a family {Pi(alpha)}(alpha) of probability measures of the Gibbs form, which are invariant under the flow. The Gibbs exponent H is given by the renormalized energy. These measures are supported by the space of configuration Gamma, i.e. the fluid vorticity is concentrated in a finite number of distinct points. Properties of a deterministic vortex dynamics having Pi(alpha) as invariant measure are investigated; in particular Markov uniqueness is proven. The classical (pre-)Dirichlet form associated to Pi(alpha) is also introduced and analyzed.
Invariant Gibbs measures for the 2D vortex motion of fluids
FERRARIO, BENEDETTA
2004-01-01
Abstract
Invariant quantities of the classical motion of an ideal incompressible fluid in a two-dimensional bounded domain are used to construct a family {Pi(alpha)}(alpha) of probability measures of the Gibbs form, which are invariant under the flow. The Gibbs exponent H is given by the renormalized energy. These measures are supported by the space of configuration Gamma, i.e. the fluid vorticity is concentrated in a finite number of distinct points. Properties of a deterministic vortex dynamics having Pi(alpha) as invariant measure are investigated; in particular Markov uniqueness is proven. The classical (pre-)Dirichlet form associated to Pi(alpha) is also introduced and analyzed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
