Related papers: Point vortices for inviscid generalized surface qu…
We consider a numerical approach for a covariant generalised Navier-Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterised by…
In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
For point vortices in the plane, we consider the correlation coefficient of Ovchinnikov and Sigal. Generalising a result by Esposito, we show that it vanishes for all vortex equilibria.
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
In this paper we prove that the branch curve of a general projection of a surface to the plane is irreducible, with only nodes and cusps.
In this paper, we study a point-hyper plane incidence theorem in matrix rings, which generalizes all previous works in literature of this direction.
In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and…
This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the…
We consider the problem of when a closed orientable hyperbolic surface admits a totally geodesic embedding into a closed orientable hyperbolic 3-manifold; given a finite isometric group action on the surface, we consider in particular…
In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…
We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.
In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1.In general, the conditions for a topological vector space to be quasi-point-separable is not very…
We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.
We prove a Cayley-Bacharach-type theorem for points in projective space $\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This is made possible by new bounds on the growth of the Hilbert function of almost complete…
We study the existence of doubly connected rotating patches for the inviscid surface quasi- geostrophic equation left open in \cite{HHH}. By using the approach proposed by \cite{CCGS} we also prove that close to the annulus the boundaries…
We compare an inviscid vortex sheet model with continuous leading-edge shedding with direct Navier-Stokes simulations over a wide range of unsteady plate motions at moderate Reynolds number ($\mathrm{Re} \approx 1000$). Approximately $70$…
The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…
We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a…
We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection…
In this paper, we propose a geometrical proof of the generalized mirror transformation of genus 0 Gromov-Witten invariants of degree k hypersurface in CP^{N-1}.