Related papers: Vortex stretching and criticality for the 3D NSE
Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energy equality for weak solutions in a large class of function…
We study controllability issues for the Navier-Stokes Equation on a two dimensional rectangle with so-called Lions boundary conditions. Rewriting the Equation using a basis of harmonic functions we arrive to an infinite-dimensional system…
Rotation significantly influences the stability characteristics of both laminar and turbulent shear flows. This study examines the stability threshold of the three-dimensional Navier-Stokes equations with rotation, in the vicinity of the…
In this paper we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the…
We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove…
We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier-Stokes equations where…
In this paper, we establish the well-posedness results of the three dimensional stationary Navier--Stokes equations (SNS) in some critical hybrid type Besov spaces with respect to the scaling invariant structure of (SNS). Although such…
We study the solution to the two-dimensional incompressible Navier-Stokes equations arising from a sum of Dirac masses in a particular co-rotating configuration. This configuration consists of a polygonal vortex crystal with or without a…
In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…
The Navier-Stokes-Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested…
We prove that the incompressible Navier-Stokes equations exhibit norm inflation in $\dot B^{s}_{p,q}(\mathbb{R}^3)$ with smooth, compactly supported initial data. Such norm inflation is shown in all supercritical $\dot B^{s}_{p,q} $ near…
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like…
We study the regularity criteria for weak solutions to the $3D$ incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the boundary effects. A boundary regularity theorem is proved on…
We consider point vortex systems on the two dimensional torus perturbed by environmental noise. It is shown that, under a suitable scaling of the noises, weak limit points of the empirical measures are solutions to the vorticity formulation…
We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in the half space. The whole space analogue, due to Jia and \v{S}ver\'ak [J\v{S}14], is a central tool in two of the authors' recent work on…
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…
Time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small…
We consider the Navier-Stokes equation on a two dimensional torus with a random force, white noise in time and analytic in space, for arbitrary Reynolds number $R$. We prove probabilistic estimates for the long time behaviour of the…