The membrane technology has attracted increasing attention in the field of separation and
desalination due to its high efficiency, energy saving, environmental protection, and other …

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) …

Singular perturbations occur when a small coefficient affects the highest order derivatives in
a system of partial differential equations. From the physical point of view, singular …

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 …

Due to degeneracy near the boundary, the question of high regularity for solutions to the
steady Prandtl equations has been a longstanding open question since the celebrated work …

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 …

In this article we establish the validity of Prandtl layer expansions around Euler flows which
are not shear. The presence of nonshear flows at the leading order creates a scaling of …

This paper is concerned with the stationary problem of an aero-taxis system with physical
boundary conditions proposed by Tuval et al (2005 Proc. Natl Acad. Sci. 102 2277–82) to …

Singularly perturbed boundary value problems pose a significant challenge for their
numerical approximations because of the presence of sharp boundary layers. These sharp …

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 …