相关论文: Separation for the stationary Prandtl equation

In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case of adverse pressure gradient, an important physical…

We demonstrate the existence of an open set of data which exhibits \textit{reversal} and \textit{recirculation} for the stationary Prandtl equations (data is taken in an appropriately defined product space due to the simultaneous forward…

In this paper, we study the back flow of the two-dimensional unsteady Prandtl boundary layer under an adverse pressure gradient. The occurrence of back flow is an important physical event in the evolution of boundary layer, which eventually…

Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex…

We consider the Stokes system in the half-space with localized boundary data. We prove that a boundary layer separation point exists provided that a certain singular integral determined by the boundary data is negative. On the other hand,…

In this article, the boundary singularity for stationary solutions of the linearized Boltzmann equation with cut-off inverse power potential is analyzed. In particular, for cut-off hard-potential cases, we establish the asymptotic…

We study a large class of stochastic $p$-Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existence, uniqueness, and regularity of variational solutions.…

We investigate the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions' collision kernel. Both, the physical as well as the velocity space, are assumed to be bounded. Existence and uniqueness of a stationary…

This work presents an asymptotic stability result concerning the self-similar Blasius profiles $[\bar{u}, \bar{v}]$ of the stationary Prandtl boundary layer equation. Initially demonstrated by Serrin \cite{MR0282585}, the profiles…

We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in $L^p$-based function spaces for $1 < p < \infty$ under the separation condition of the…

This is the first part of a two paper sequence in which we prove the global-in-x stability of the classical Prandtl boundary layer for the 2D, stationary Navier-Stokes equations. In this part, we provide a construction of an approximate…

Oleinik's \emph{no back-flow} condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain $R\subset \mathbb{R}^2$. It also allowed us to find a limit formula for Dorodnitzyn's stationary…

This paper is concerned with existence, uniqueness and stability of the solution for the 3D Prandtl equation in a polynomial weighted Sobolev space. The main novelty of this paper is to directly prove the long time well-posedness to 3D…

We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…

The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($\beta \in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $\beta \frac{\pi}{2}$. The most…

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…

Considering the boundary layer problem in the case of two-dimensional flow past a wedge with the wedge angle $\varphi=\pi\frac{2m}{m+1}$, Oleinik and Samokhin obtained the local well-posedness results for $m \geq 1$. In this paper, we…

We study the existence and uniqueness of a solution to a linear stationary convection-diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of…

In the lines of a recent paper by Gerard-Varet and Dormy, we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary shear flows, we show that for some linearizations of the Prandtl…

We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, we assume that the initial datum $u_0$ is monotone on a…