Related papers: Analysis of complex singularities in high-Reynolds…
We study the dynamics of the two dimensional Navier-Stokes equations linearized around a shear flow on a (non-square) torus which possesses exactly two non-degenerate critical points. We obtain linear inviscid damping and vorticity…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…
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…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…
We consider the inviscid unsteady Prandtl system in two dimensions, motivated by the fact that it should model to leading order separation and singularity formation for the original viscous system. We give a sharp expression for the maximal…
We present a formal, approximate model for singularity formation in classical fluid dynamics in three dimensions. The construction utilizes an approximation of local two-dimensionality to study an anti-parallel hairpin vortex structure with…
This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…
High Reynolds numbers Navier-Stokes equations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global…
In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we…
We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
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…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
The planar problem of a viscous laminar flow around elliptical cylinders under angle of attack is considered. From the solution of the laminar boundary layer equations using the Loytsyansky local similarity method, the shear stress at the…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We present a systematic numerical investigation of bifurcations in the two-dimensional incompressible Navier-Stokes flow past a confined circular cylinder. The results indicate that there is a qualitative correspondence between changes in…