Related papers: Boundary Layer Expansions for the Stationary Navie…
In this work, we establish the convergence of 2D, stationary Navier-Stokes flows, $(u^\epsilon, v^\epsilon)$ to the classical Prandtl boundary layer, $(\bar{u}_p, \bar{v}_p)$, posed on the domain $(0, \infty) \times (0, \infty)$:…
Let the viscosity $\varepsilon \rightarrow 0$ for the 2D steady Navier-Stokes equations in the region $0\leq x\leq L$ and $0\leq y<\infty$ with no slip boundary conditions at $y=0$. For $L<<1$, we justify the validity of the steady Prandtl…
In this paper, we consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in $(0,L)\times\mathbb{R}^+$ with non-slip boundary conditions. By estimating the stream-function of the remainder, we justify the validity of the…
This paper is concerned with the validity of the Prandtl boundary layer theory in the inviscid limit of the steady incompressible Navier-Stokes equations, which is an extension of the pioneer paper (Y. Guo et al., 2017, Ann. PDE) from a…
The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: $\nu \to 0$. In \cite{Grenier}, one of the authors proved that there exists no asymptotic expansion involving one Prandtl's…
In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier Stokes equations. We then recall classical physical instability results, and give a short educational…
We consider the problem of the stability of the Navier-Stokes equations in $\mathbb{T}\times \mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \cite{greniernguyen}, the authors prove an $L^{\infty}$…
Assume no-slip boundary conditions for the velocity field and either insulated or Dirichlet boundary conditions for the temperature field in a steady compressible fluid. In the inviscid limit $\v \rightarrow 0$, we develop a mathematical…
In this three-part monograph, we prove that steady, incompressible Navier-Stokes flows posed over the moving boundary, $y = 0$, can be decomposed into Euler and Prandtl flows in the inviscid limit globally in $[1,\infty) \times [0,\infty)$,…
This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid…
We investigate the stability of boundary layer solutions of the two-dimensional incompressible Navier-Stokes equations. We consider shear flow solutions of Prandtl type : $$ u^\nu(t,x,y) \, = \, \big (U^E(t,y) +…
This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\times \mathbb{R}_{+}$, assuming…
We study the $L^{\infty}$ stability of the 2D Navier-Stokes equations with a viscosity-dependent Navier boundary condition around shear profiles which are linearly unstable for the Euler equation. The dependence from the viscosity is given…
In $1904$, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to $0$. His Ansatz was that the solution of Navier Stokes…
This paper concerns the large Reynold number limits and asymptotic behaviors of solutions to the 2D steady Navier-Stokes equations in an infinitely long convergent channel. It is shown that for a general convergent infinitely long nozzle…
Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by…
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…
In this paper, we establish the vanishing viscosity limit result of the 2D stationary Navier-Stokes equations outside a rotating disc. On the boundary of the disc, the fluid is subjected to a small perturbation of a non zero rotation of…
We investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is an improved Lipschitz regularity estimate at scales larger…
We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1,…