Related papers: Statistical properties of stochastic 2D Navier-Sto…
We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of…
We explore the advection-diffusion of a passive vector described by $\partial_t u + U \cdot \nabla u = - \nabla p + \nu \Delta u$, where both $U$ and $u$ are divergence-free velocity fields. We approach this equation from an input/output…
We approximate a two--phase model by the compressible Navier-Stokes equations with a singular pressure term. Up to a subsequence, these solutions are shown to converge to a global weak solution of the compressible system with the congestion…
Building upon the well-posedness results in \cite{snse1}, in this note we prove the existence of invariant measures for the stochastic Navier-Stokes equations with stable L\'evy noise. The crux of our proof relies on the assumption of…
We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…
This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of…
We study the statistical properties of stationary, isotropic and homogeneous turbulence in two-dimensional (2D) flows, focusing on the direct cascade, that is on wave-numbers large compared to the integral scale, where both energy and…
We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centers. At a dynamical level, the hidden…
We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by…
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importance, their behavior in turbulent regimes remains incompletely…
We positively answer Question 2.2 and Question 2.3 in [Bru\`e, De Lellis, 2023] in dimension $4$ by building new examples of solutions to the forced $4d$ incompressible Navier-Stokes equations, which exhibit anomalous dissipation, related…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
In this paper, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent variables and a method of moving frame for solving the three dimensional Navier-Stokes equations. Seven families of…
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of…
For wavenumbers k such that k * alpha > 1, corresponding to spatial scales smaller than alpha, there are three candidate power laws for the energy spectrum of the Navier-Stokes-alpha model, corresponding to three possible dynamical eddy…
We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of…
We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…
In this paper, we establish a moderate deviation principle for an abstract nonlinear equation forced by random noise of L\'evy type. This type of equation covers many hydrodynamical models, including stochastic 2D Navier-Stokes equations,…
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems,…
In the present paper, we study the fractional incompressible Stochastic Navier-Stokes equation on $\mathbb{R}^2$, formally defined as \[ \partial_t v = -\tfrac12 (-\Delta)^\theta v - \lambda v \cdot \nabla v + \nabla p - \nabla^{\perp}…