Related papers: Algebraic construction of a Nambu bracket for the …
We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten…
Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for…
A kinematical description of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations…
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…
In this note, we consider a viscous incompressible fluid in a finite domain in both two and three dimensions, and examine the question of determining degrees of freedom (projections, functionals, and nodes). Our particular interest is the…
We introduce the notion of the modular class of a Lie algebroid equipped with a Nambu structure. In particular, we recover the modular class of a Nambu-Poisson manifold $M$ with its Nambu tensor $\Lambda$ as the modular class of the tangent…
In this paper we will prove that the vorticity belongs to L1(0; T ; L2(\Omega)) for 3D incompressible Navier-Stokes equation with periodic initial-boundary value conditions, then the existence of a global smooth solution is obtained. Our…
Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…
Through the Ginzburg-Landau and the Navier-Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of…
A variational formulation is introduced for the Oseen equations written in terms of vor\-ti\-city and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions…
Vorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the…
The phenomenon of finite time blow-up in hydrodynamic partial differential equations is central in analysis and mathematical physics. While numerical studies have guided theoretical breakthroughs, it is challenging to determine if the…
In this paper, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane with Navier-slip boundary conditions. We prove that the total vorticity will…
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A new relaxation equation is obtained for the evolution of the…
The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box $[0,\,L]^{3}$ is addressed through four sets of numerical simulations that calculate a new set of variables defined by $D_{m}(t) =…
Based on our recent work on Quantum Nambu Mechanics $\cite{af2}$, we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices…