arXiv subjects

Alexandra Symeonides

Publications and source records attributed to Alexandra Symeonides.

3 recordsLinked to original sources

arXiv2017

On a non-periodic modified Euler equation: existence and quasi-invariant measures

We consider a modified Euler equation on $\mathbb R^2$. We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct Gibbs-type measures on function spaces which are quasi-invariant for the Euler flow. Almost everywhere with respect to such measures (and, in particular, for less regular initial conditions), the flow is shown to be also globally defined.

math.AP↗

arXiv2017

Invariant measures for the non-periodic two-dimensional Euler equation

We construct Gaussian invariant measures for the two-dimensional Euler equation on the plane. We show the existence of solution with initial conditions in the support of the measures, namely $H^β_{loc}(\R^2)$ with $β<-1$. Uniqueness and continuity of the velocity flow are proved.

math.AP↗

arXiv2016

Invariant measures for the two-dimensional averaged-Euler equations

We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the energy is also constructed, as well as the corresponding flow. Poincar\'e recurrence theorem is used to show that the flow returns infinitely many times in a neighbourhood of the initial state.

math.AP↗