Related papers: Euler-Poincar\'e Formulation of Barotropic Fluids …
The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for…
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…
One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long…
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically symmetric flows. The one-dimensional flow of a polytropic gas…
A connection between solutions of the relativistic d-brane system in (d+1) dimensions with the solutions of a Galileo invariant fluid in d-dimensions is by now well established. However, the physical nature of the light-cone gauge…
We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a…
We discuss general bosonic configurations of four-dimensional N=2 supergravity coupled to vector multiplets in (t,s) space-time. The supergravity theories with Euclidean and neutral signature are described by the so-called para-special…
We study the holographic hydrodynamics in the Einstein-Gauss-Bonnet(EGB) gravity in the framework of the large $D$ expansion. We find that the large $D$ EGB equations can be interpreted as the hydrodynamic equations describing the conformal…
We focus on the spatial discretization produced by the Variational Particle-Mesh (VPM) method for a prototype fluid equation the known as the EPDiff equation}, which is short for Euler-Poincar\'e equation associated with the diffeomorphism…
The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented. They provide us with the class of solutions of the Euler…
In this paper we are interested in geometric aspects of blowup in the axisymmetric 3D Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
In this article, we combine V. Arnold's celebrated approach via the Euler-Arnold equation -- describing the geodesic flow on a Lie group equipped with a right-invariant metric \cite{Arnold66} -- with his formulation of the motion of a…
Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological…
We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or…
In this article we write the equations of barotropic compressible fluid mechanics as a geodesic equation on an infinite-dimensional manifold. The equations are given by \begin{align} u_t + \nabla_uu = -\frac{1}{\rho} \grad p \\ \rho_t +…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
We here investigate a modification of the compressible barotropic Euler system with friction, involving a fuzzy nonlocal pressure term in place of the conventional one. This nonlocal term is parameterized by $\epsilon$ > 0 and formally…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
In view of the recent interest in reproducing holographically various properties of conformal fluids, we review the issue of vorticity in the context of AdS/CFT. Three-dimensional fluids with vorticity require four-dimensional bulk…