Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-
Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial …

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 develop a new approach to study the well-posedness theory of the Prandtl equation in
Sobolev spaces by using a direct energy method under a monotonicity condition on the …

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 …

The concern of this paper is the Cauchy problem for the Prandtl equation. This problem is
known to be well-posed for analytic data, or for data with monotonicity properties. We prove …

In this paper we give examples of nonlinearly unstable solutions of Euler equations in the
whole space ℝ2, the half space ℝ× ℝ+, the periodic strip ℝ× 𝕋, the strip ℝ×[− 1, 1], and the …

We consider the Navier‐Stokes equations for viscous incompressible flows in the half‐plane
under the no‐slip boundary condition. By using the vorticity formulation we prove the local …

In this paper we establish a global existence of weak solutions to the two-dimensional
Prandtl's system for unsteady boundary layers in the class considered by Oleinik (J. Appl …

Euler equations of incompressible fluids use and enrich many branches of mathematics,
from integrable systems to geometric analysis. They present important open physical and …