Related papers: Euler-Poincar\'{e} equations for anelastic fluid f…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be…
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A…
We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free- boundary, constrained by the condition of…
In this manuscript, we extend Constantin-Iyer's Lagrangian formulation of Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is naturally derived from a stochastic…
The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
Euler-Poincare equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the…
We consider the vorticity formulation of the Euler equations describing the flow of a two-dimensional incompressible ideal fluid on the sphere. Zeitlin's model provides a finite-dimensional approximation of the vorticity formulation that…
This paper reports a theoretical and numerical framework to model nonlinear waves in elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed include the continuity equation, the momentum equation, and an…
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we…
We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation…
We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid motion is…
Following Arnold's geometric interpretation, the Euler equations of an incompressible fluid moving in a domain D are known to be the optimality equation of the minimizing geodesic problem along the group of orientation and volume preserving…
This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions…
This note is devoted to the linear stability of the Couette flow for the non-isentropic compressible Euler equations in a domain $\mathbb{T}\times \mathbb{R}$. Exploiting the several conservation laws originated from the special structure…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…
We consider the calculation of Euler--Lagrange systems of ordinary difference equations, including the difference Noether's Theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We…
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The…