Related papers: Anomalous dissipation and Euler flows
We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the…
In this paper, we are concerned with the initial-Neumann boundary value problem of the Schr\"{o}dinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}^2$. By adopting a novel method due to B. Chen and Y.D.…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
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…
We study the Hull-Strominger system and the Anomaly flow on a special class of 2-step solvmanifolds, namely the class of almost-abelian Lie groups. In this setting, we characterize the existence of invariant solutions to the Hull-Strominger…
We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling…
We prove that any sequence of vanishing viscosity Leray-Hopf solutions to the periodic two-dimensional incompressible Navier-Stokes equations does not display anomalous dissipation if the initial vorticity is a measure with positive…
We simulate stellar convection at high Reynolds number (Re$\lesssim$7000) with causal time stepping but no explicit viscosity. We use the 3D Euler equations with shock capturing (Colella & Woodward 1984). Anomalous dissipation of turbulent…
The energy dissipation in the inviscid limit is a central problem in turbulence theory. Kolmogorov's K41 theory predicts a positive dissipation rate independent of viscosity -- a phenomenon known as anomalous dissipation. Bru\'e and De…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
For any $\epsilon >0$ we show the existence of continuous periodic weak solutions $v$ of the Euler equations which do not conserve the kinetic energy and belong to the space $L^1_t (C_x^{\frac{1}{3}-\epsilon})$, namely $x\mapsto v (x,t)$ is…
The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian,…
We present a new approach to determine numerically the statistical behavior of small-scale structures in hydrodynamic turbulence. Starting from the functional integral representation of the random-force-driven Burgers equation we show that…
We show that H\"{o}lder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples that strictly dissipate kinetic energy. The collection of…
Scaling in the dynamical properties of complex many-body systems has been of strong interest since turbulence phenomena became the subject of systematic mathematical studies. In this article, dynamical critical phenomena far from…
In this paper, we formulated the non-steady flow due to the uniformly accelerated and rotating circular cylinder from rest in a stationary, viscous, incompressible and micropolar fluid. This flow problem is examined numerically by adopting…
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…
We accomplish two major tasks. First, we show that the turbulent motion at large scales obeys Gaussian statistics in the interval 0 < Rlambda < 8.8, where Rlambda is the microscale Reynolds number, and that the Gaussian flow breaks down to…