Related papers: A geometric characterization of potential Navier-S…
We use recent developments in the theory of finite-time dynamical systems to objectively locate the material boundaries of coherent vortices in two-dimensional Navier--Stokes turbulence. We show that these boundaries are optimal in the…
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a…
We study the two-dimensional Navier-Stokes system on a flat cylinder with the usual Dirichlet boundary conditions for the velocity field u. We formulate the problem as an infinite system of ODE's for the natural Fourier components of the…
We show that if v is an axially symmetric suitable weak solution to the Navier Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg) such that the radial component of v has a higher regularity (i.e. satisfies weighted…
We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity…
The paper proves existence of a large class of smooth solutions to the incompressible Navier-Stokes equations in the three dimensional space. The viscosity coefficient is put to be $1$. Our result points a new class of regular solutions…
We consider the global approximate controllability of the two-dimensional incompressible Navier-Stokes system driven by a physically localized and degenerate force. In other words, the fluid is regulated via four scalar controls that depend…
In this paper we aim to construct a very weak solution to the steady two-dimensional Navier-Stokes equations which is affected by an external force induced by a point vortex on the unit disk. Such a solution is also the form of…
The goal of this paper is to theoretically investigate the origin of the standing wave-like perturbation observed on the vortex rings falling through another liquid. We simplified the Navier-Stokes equation based on observational evidence…
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and…
We first show the equivalence of two classes of generalized suitable weak solutions to the 3D incompressible Navier-Stokes equations allowing distributional pressure, the class of dissipative weak solutions and local suitable weak…
We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
A local anisotropic geometric measure-type condition on the super-level sets of solutions to the 3D NSE preventing the formation of finite-time singularity is presented; essentially, local one-dimensional sparseness of the regions of…
The aim of the note is to proof a regularity result for weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$. It reads that, in a sense, the number of singular points at each time is at most finite. Our…
This paper proposes a solution to Stokes' paradox for asymptotically uniform viscous flow around a cylinder. The existence of a {\it global} stream function satisfying a perturbative form of the two-dimensional Navier-Stokes equations for…
We consider the modified Navier-Stokes equations in R3 describing the motion of a fluid in the presence of a rotating rigid body. Weighted Sobolev spaces are used to describe the behavior of solutions at large distances. Under suitable…
We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…