Let the viscosity ε→ 0 ε→0 for the 2D steady Navier‐Stokes equations in the region 0≤ x≤
L 0≤x≤L and 0≤ y<∞ 0≤y<∞ with no slip boundary conditions at y= 0 y=0. For L<< 1 …

The aim of this book is to provide beginning graduate students who completed the first two
semesters of graduate-level analysis and PDE courses with a first exposure to the …

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) …

The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics
system with Prandtl boundary layer expansion when no-slip boundary condition is imposed …

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes
equations modeling viscous incompressible flows converge to solutions of the Euler …

In this paper, we prove that separation occurs for the stationary Prandtl equation, in the case
of adverse pressure gradient, for a large class of boundary data at x= 0 x=0. We justify the …

We address the local well-posedness of the hydrostatic Navier–Stokes equations. These
equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the …

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 …

The well-posedness of the three space dimensional Prandtl equations is studied under
some constraint on its flow structure. Together with the instability result given in [28], it gives …

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 …