Related papers: A consistent stochastic large-scale representation…
We prove existence of infinitely many stationary solutions as well as ergodic stationary solutions for the stochastic Navier-Stokes equations on $\mathbb{T}^2$ \begin{align*} \dif u+\div(u\otimes u)\dif t+\nabla p\dif t&=\Delta u\dif t +…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
We are concerned with the (stochastic) Lagrangian trajectories associated with Euler or Navier-Stokes equations. First, in the vanishing viscosity limit, we establish sharp non-uniqueness results for positive solutions to transport…
We consider a stochastic model which describes the motion of a 2D incompressible fluid in a unbounded domain with viscosity and memory effects. This model is different from the classical stochastic Navier-Stokes-Voigt equations due to the…
A numerical study is presented to analyze the thermal mechanisms of unsteady, supersonic granular flow, by means of hydrodynamic simulations of the Navier-Stokes granular equations. For this purpose a paradigmatic problem in granular…
We investigate fractional stochastic Navier-Stokes equations in $d\ge 3$, driven by the random force $(-\Delta)^{\frac{\theta}{2}}\xi$ which, as we show, corresponds to a fractional version of the Landau-Lifshitz random force in the physics…
In this paper, we consider a stochastic nonlinear formulation of classical coastal waves models under location uncertainty (LU). In the formal setting investigated here, stochastic versions of the Serre-Green- Nagdi, Boussinesq and…
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved…
We prove that a popular classical implicit-explicit scheme for the 2D incompressible Navier--Stokes equations that treats the viscous term implicitly while the nonlinear advection term explicitly is long time stable provided that the time…
We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate…
In this paper, we construct martingale suitable weak solutions for $3$-dimensional incompressible stochastic Navier-Stokes equations with generally non-linear noise. In deterministic setting, as widely known, ``suitable weak solutions'' are…
In this paper, we show that suitable transport noises produce anomalous dissipation of both enstrophy of solutions to 2D Navier-Stokes equations and of energy of solutions to diffusion equations in all dimensions. The key ingredients are…
In the current state of the art regarding the Navier--Stokes equations, the existence of unique solutions for incompressible flows in two spatial dimensions is already well-established. Recently, these results have been extended to models…
The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…
We propose a novel method for the direct numerical simulation of interfacial flows involving large density contrasts, using a Volume-of-Fluid method. We employ the conservative formulation of the incompressible Navier-Stokes equations for…
We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved…
The aim of this work is to prove an existence and uniqueness result of Kato-Fujita type for the Navier-Stokes equations, in vorticity form, in $2-D$ and $3-D$, perturbed by a gradient type multiplicative Gaussian noise (for sufficiently…
We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of…