Related papers: Integrability in Fluid Dynamics
It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold.…
We present a comprehensive Eulerian (Hamiltonian) framework for relativistic fluid dynamics in curved spacetimes, with emphasis on Schwarzschild geometry. The key innovation lies in the consistent use of density and three-velocity fields,…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of…
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe…
In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.
The affine motion of two-dimensional (2d) incompressible fluids surrounded by vacuum can be reduced to a completely integrable and globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in ${\rm…
It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric…
New exact solutions of relativistic perfect fluid hydrodynamics are described, including the first family of exact rotating solutions. The method used to search for them is an investigation of the relativistic hydrodynamical equations and…
The evolution of piecewise constant distributions of a conserved quantity related to the frozen-in canonical vorticity in effectively two-dimensional incompressible ideal EMHD flows is analytically investigated by the Hamiltonian method.…
Shape Dynamics is a 3D conformally invariant theory of gravity which possesses a large set of solutions in common with General Relativity. When looked closely, these solutions are found to behave in surprising ways, so in order to probe the…
Hyperfluid model is reconstructed on the basis of its action free from any external constraints, regarding the hyperfluid as a self-consistent classical field. Intrinsic hypermomentum is no more a given variable, but arises purely from the…
A very intuitive description of nucleus-nucleus collision phenomena is provided by the relativistic fluid dynamics. We consider a 1+1 dimensional relativistic imperfect fluid flow to approximate the high energy heavy ion collision. The…