Related papers: On the Ricci-flat metric for the Navier-Stokes equ…
We introduce a metric notion of Ricci curvature for $PL$ manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.
We introduce new classes of solutions to the three dimensional Navier-Stokes equations in the whole and half spaces that add rotational correction to self-similar and discretely self-similar solutions. We construct forward solutions in…
We construct explicit complete Ricci-flat metrics on the total spaces of certain vector bundles over flag manifolds of the group $SU(n)$, for all K\"ahler classes. These metrics are natural generalizations of the metrics of Candelas-de la…
We shall prove dispersive and smoothing estimates for Bochner type laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. These estimates will be used to prove Fujita-Kato type…
In this short article, we improve the dynamical stability and instability results for Ricci-flat metrics under Ricci flow proved by Sesum and Haslhofer, getting rid of the integrability assumption.
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this…
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a…
We give new a priori assumptions on weak solutions of the Navier-Stokes equation so as to be able to conclude that they are smooth. The regularity criteria are given in terms of mixed radial-angular weighted Lebesgue space norms.
We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
In $N(k)$-contact metric manifolds and/or $(k,\mu)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $\xi $ are studied.
For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional curvature and one of positive definite Ricci tensor to one with…
We derive, under a technical assumption, the first variation formula for the eigenvalues of the Laplacian on a closed manifold evolving by the Ricci flow and give some applications.
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we…
We obtain Ricci flat K\"ahler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
In this paper, we study several types of geometric problems related to the Ricci curvature on noncompact complex manifolds, such as the existence of K\"{a}hler-Einstein metrics on complete K\"{a}hler manifolds with negative Ricci curvature,…
The Navier-Stokes equations are considered by the use of the method of Lagrangians with covariant derivatives (MLCD) over spaces with affine connections and metrics. It is shown that the Euler-Lagrange equations appear as sufficient…