A characterization of the symmetric steady water waves in terms of the underlying flow

In this paper we present a characterization of the symmetric rotational periodic gravity water waves of finite depth and without stagnation points in terms of the underlying flow. Namely, we show that such a wave is symmetric and has a single crest and trough per period if and only if there exists a vertical line within the fluid domain such that all the fluid particles located on that line minimize there simultaneously their distance to the fluid bed as they move about. Our analysis uses the moving plane method, sharp elliptic maximum principles, and the principle of analytic continuation.Comment: 10 page

On the existence of steady periodic capillary-gravity stratified water waves

We prove the existence of small steady periodic capillary-gravity water waves for general stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the governing equations. This is achieved by using bifurcation theory and estimates based on the ellipticity of the system, where we regard, in turn, the mass-flux and surface tension as bifurcation parameters.Comment: 17 pages, to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sc

A gradient flow approach to a thin film approximation of the Muskat problem

A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two Liapunov functionals turns out to be a central tool to obtain the needed regularity to identify the Euler-Lagrange equation in the variational scheme

THE REFORM OF NATIONAL BANK OF ROMANIA AFTER ACCESSION TO EU: CHALLENGES AND PERSPECTIVES

In January 2007, Romania had become a member of the European Union and the National Bank of Romania a member of The European System of Central Banks (ESCB). This event was a confirmation of the success of Romanian reforms, but, on the other hand, it was a beginning of a new stage in the process of accomplishing the nominal and real convergence conditions, set in the Maastricht Treaty. In this study we have done some considerations about the NBR's reform performances before and after EU accession and, also, we have talked about the main challenges and perspectives for Romanian central bank in the new economic environment imposed by the integration process.European integration, central bank, reform, challenges, perspectives