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 …

We prove local existence and uniqueness for the two‐dimensional Prandtl system in
weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not …

We investigate the stability of boundary layer solutions of the 2-dimensional incompressible
Navier–Stokes equations. We consider shear flow solutions of Prandtl type: u ν (t, x, y)=(UE …

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 …

We show the local in time well-posedness of the Prandtl equations for data with Gevrey 2
regularity in x and Sobolev regularity in y. The main novelty of our result is that we do not …

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 …

We consider the Prandtl boundary layer equations on the half plane, with initial datum that
lies in a weighted H 1 space with respect to the normal variable, and is real-analytic with …

We study the well‐posedness theory for the MHD boundary layer. The boundary layer
equations are governed by the Prandtl‐type equations that are derived from the …

In this paper, we investigate the long time existence and uniqueness of small solution to d,
for d= 2, 3, dimensional Prandtl system with small initial data which is analytic in the …

In the first part of the paper we provide a new classification of incompressible fluids
characterized by a continuous monotone relation between the velocity gradient and the …