[LLIBRE][B] The water waves problem: mathematical analysis and asymptotics

D Lannes - 2013 - books.google.com
Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

Spectral stability of Prandtl boundary layers: an overview

E Grenier, Y Guo, TT Nguyen - Analysis, 2015 - degruyter.com
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 …

Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

M Sammartino, RE Caflisch - Communications in mathematical physics, 1998 - Springer
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 …

On the ill-posedness of the Prandtl equation

D Gérard-Varet, E Dormy - Journal of the American Mathematical Society, 2010 - ams.org
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 …

On the nonlinear instability of Euler and Prandtl equations

E Grenier - Communications on Pure and Applied Mathematics …, 2000 - Wiley Online Library
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 …

Local‐in‐time existence and uniqueness of solutions to the Prandtl equations by energy methods

N Masmoudi, TK Wong - Communications on Pure and Applied …, 2015 - Wiley Online Library
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 …

Well-posedness of the Prandtl equation in Sobolev spaces

R Alexandre, YG Wang, CJ Xu, T Yang - Journal of the American …, 2015 - ams.org
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 …

On the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half‐plane

Y Maekawa - Communications on Pure and Applied …, 2014 - Wiley Online Library
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 …

On the Euler equations of incompressible fluids

P Constantin - Bulletin of the American Mathematical Society, 2007 - ams.org
Euler equations of incompressible fluids use and enrich many branches of mathematics,
from integrable systems to geometric analysis. They present important open physical and …

On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions

T Clopeau, A Mikelic, R Robert - Nonlinearity, 1998 - iopscience.iop.org
The vanishing viscosity limit is considered for the incompressible 2D Navier-Stokes
equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's …