Related papers: Rigorous results in space-periodic two-dimensional…
We provide a first-principles approach to turbulence by employing the electrodynamics of continuous media at the viscous limit to recover the Navier-Stokes equations. We treat oscillators with two orthogonal angular momenta as a spin…
Material elements - which are lines, surfaces, or volumes behaving as passive, non-diffusive markers - provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate…
We propose a two-dimensional generalization of Constantin-Lax-Majda model [2]. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line…
We propose a theoretical framework where the dissipative structures of turbulence emerge from microscopic path uncertainty. By modeling fluid parcels as stochastic tracers governed by the Schr\"odinger Bridge (SB) variational principle, we…
We consider a fluid governed by the randomly forced 2D Navier-Stokes system. It is assumed that the force is bounded, acts directly only on a small number of Fourier modes, and satisfies some natural decomposability and observability…
This paper investigates the stochastic tamed 3D Navier-Stokes equations with locally weak monotonicity coefficients in the whole space as well as in the three-dimensional torus, which play a crucial role in turbulent flows analysis. A…
Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy…
We consider freely decaying two-dimensional isotropic turbulence. It is usually assumed that, in such turbulence, the energy spectrum at small wave number, takes the form, where is the two-dimensional version of Loitsyansky's integral. In…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in $\R^3$. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the $\alpha^{th}$-order fractional…
The randomly driven Navier-Stokes equation without pressure in d-dimensional space is considered as a model of strong turbulence in a compressible fluid. We derive a closed equation for the velocity-gradient probability density function. We…
In this study we investigate the statistics of two-dimensional stationary turbulence using a Markovian forcing scheme, which correlates the forcing process in the current time step to the previous time step according to a defined memory…
We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.
We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with…
We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the…
The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…
We inquire the statistical properties of the pair formed by the Navier-Stokes equation for an incompressible velocity field and the advection-diffusion equation for a scalar field transported in the same flow in two dimensions (2d). The…
We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair…
The issue of why computational resolution in Navier-Stokes turbulence is so hard to achieve is addressed. It is shown that Navier-Stokes solutions can potentially behave differently in two distinct regions of space-time $\mathbb{R}^{\pm}$…
Through Ginzburg-Landau and Navier-Stokes equations, we study turbulence phenomena for viscous incompresible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of classical and…
We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $\Lambda$ to distinguish between vortical and extensional regions. We then use a direct numerical…