Related papers: Non-unique ergodicity for deterministic and stocha…

In this paper we study the uniqueness property of solutions to the steady incompressible Euler equations with perturbations in $\Bbb R^N$. Our perturbations include as special cases the Euler equations with a `single signed' nonlinear term,…

We study statistical solutions of the incompressible Euler equations in two dimensions with vorticity in $L^p$, $1\leq p \leq \infty$, and in the class of vortex-sheets with a distinguished sign. Our notion of statistical solution is based…

The existence of weak solutions to the stationary Navier-Stokes equations in the whole plane $\mathbb{R}^2$ is proven. This particular geometry was the only case left open since the work of Leray in 1933. The reason is that due to the…

In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model…

We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…

In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…

In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions…

The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…

We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the…

We prove that the steady incompressible Navier-Stokes equations with any given $(-3)$-homogeneous, locally Lipschitz external force on $\mathbb{R}^n\setminus\{0\}$, $4\leq n\leq 16$, have at least one $(-1)$-homogeneous solution which is…

The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…

A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…

The predictability of turbulent flows remains a challenging problem for mathematicians, physicists, and meteorologists. In this context, we consider the 3D incompressible Navier-Stokes equations with small-scale random forcing on…

For a prescribed deterministic kinetic energy we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D incompressible Navier-Stokes equations driven by a linear multiplicative stochastic…

We study stationary homogeneous solutions to the 3D Euler equation. The problem is motivated be recent exclusions of self-similar blowup for Euler and its relation to Onsager conjecture and intermittency. We reveal several new classes of…

We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existence of solutions to this problem was only known under special…

Singular vorticty solutions of the incompressible 3D-Euler equation are constructed which satisfy the BKM criterion (cf. [2]). The construction is done by inviscid limits of vorticity solutions of transformed incompressible Navier Stokes…

We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $L^2$ weak limit of Leray--Hopf weak solutions of the Navier-Stokes equations on any…

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a $\holderspace{k}{\alpha}$…

We establish uniform bounds and the inviscid limit in $L^p$-based Sobolev conormal spaces for the solutions of the Navier-Stokes equations with the Navier boundary conditions in the half-space. We extend the vanishing viscosity results…