[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 …
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …
Spectral stability of Prandtl boundary layers: an overview
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 …
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
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 …
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 …
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 …
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
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 …
weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not …
Well-posedness of the Prandtl equation in Sobolev spaces
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 …
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 …
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 …
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
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 …
equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's …