Related papers: Prandtl-Batchelor flows on an annulus
The problem of forced convection along an isothermal, constantly moving plate is a classical problem of fluid mechanics that has been solved for the first time in 1961 by Sakiadis (1961). Thereafter, many solutions have been obtained for…
This work is concerned with the numerical investigation of the dynamics of stopping vortex formation in the uniform flow past a wedge mounted on a wall for channel Reynolds number $Re_c=1560$. The streamfunction-vorticity ($\psi$-$\omega$)…
A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in…
In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem…
Liouville-type theorems for the steady incompressible Navier-Stokes system are investigated for solutions in a three-dimensional slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary…
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…
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…
Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…
In this paper, we study the full regularity and well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin or Dirichlet boundary condition in half space. Under Oleinik's monotonicity assumption, we prove…
This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
We study a boundary layer problem for the Navier-Stokes-alpha model obtaining a generalization of the Prandtl equations conjectured to represent the averaged flow in a turbulent boundary layer. We solve the equations for the semi-infinite…
In the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other…
We assert that the solutions to the Cauchy problem of the inviscid vorticity equation remain regular and unique for any smooth initial data of finite energy. However, the primitive formulation of the Euler equations is not well-posed, due…
This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…
The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of…
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a…