29,515 research outputs found
Geodesic Flow on the Diffeomorphism Group of the circle
We show that certain right-invariant metrics endow the infinite-dimensional
Lie group of all smooth orientation-preserving diffeomorphisms of the circle
with a Riemannian structure. The study of the Riemannian exponential map allows
us to prove infinite-dimensional counterparts of results from classical
Riemannian geometry: the Riemannian exponential map is a smooth local
diffeomorphism and the length-minimizing property of the geodesics holds.Comment: 15 page
Energy Spectrum of Quasi-Geostrophic Turbulence
We consider the energy spectrum of a quasi-geostrophic model of forced,
rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2}
valid for wave numbers that are smaller than a wave number associated to the
forcing injection scale. This upper bound separates this spectrum from the
Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a
two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical
support for the k^{-2} spectrum observed in recent experiments
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
We give an elementary proof of the global well-posedness for the critical 2D
dissipative quasi-geostrophic equation. The argument is based on a non-local
maximum principle involving appropriate moduli of continuity.Comment: 7 page
Economic and social disparities of Romania in regional and county profile
Romania's accession to the European Union imposes a new way of approaching the economic and social disparities existing nowadays both at the level of the eight development regions of the country and at the level of counties as well. The analysis of the level and evolution of these disparities can be useful to all the factors that design and put into practice strategies meant to stop the gaps widening on one hand and to fill the existing gaps among the Romanian development regions on the other hand. All these analyses are made from the perspective of Romania's process of integration into the European Union's structures.convergence objective, development regions, economic disparities, EU cohesion, Principal Components Analysis.
On a two-component -Camassa--Holm system
A novel -Camassa--Holm system is studied as a geodesic flow on a
semidirect product obtained from the diffeomorphism group of the circle. We
present the corresponding details of the geometric formalism for metric Euler
equations on infinite-dimensional Lie groups and compare our results to what
has already been obtained for the usual two-component Camassa--Holm equation.
Our approach results in well-posedness theorems and explicit computations of
the sectional curvature.Comment: 12 page
On periodic water waves with Coriolis effects and isobaric streamlines
In this paper we prove that solutions of the f-plane approximation for
equatorial geophysical deep water waves, which have the property that the
pressure is constant along the streamlines and do not possess stagnation
points,are Gerstner-type waves. Furthermore, for waves traveling over a flat
bed, we prove that there are only laminar flow solutions with these properties.Comment: To appear in Journal of Nonlinear Mathematical Physics; 15 page
Regularity of H\"older continuous solutions of the supercritical quasi-geostrophic equation
We present a regularity result for weak solutions of the 2D quasi-geostrophic
equation with supercritical () dissipation : If
a Leray-Hopf weak solution is H\"{o}lder continuous with on the time interval , then it is actually a classical solution on
Lagrangian-Eulerian Methods for Uniqueness in Hydrodynamic Systems
We present a Lagrangian-Eulerian strategy for proving uniqueness and local
existence of solutions in path spaces of limited smoothness for a class of
incompressible hydrodynamic models including Oldroyd-B type complex fluid
models and zero magnetic resistivity magneto-hydrodynamics equations
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