Feeds:
Posts
Comments

Archive for the ‘boundary layers’ Category

Emmanuel Grenier and I have just submitted this 84-page! long paper, also posted on arxiv (arXiv:1705.05323). This work is a continuation and completion of the program (initiated in Grenier-Toan1 and Grenier-Toan2) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linearized Navier-Stokes around a stationary boundary layer profile.

(more…)

Read Full Post »

The aim of this paper (arXiv:1705.04672), with E. Grenier, is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: {\nu \rightarrow 0}.  In his CPAM2000 paper, Grenier proved that there exists no Prandtl’s asymptotic expansion involving one Prandtl’s boundary layer with thickness of order {\sqrt\nu}, which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order {\nu^{3/4}}. In this paper, we point out how the stability of the classical Prandtl’s layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in {L^\infty}.  That is, either the Prandtl’s layer or the boundary sublayer is nonlinearly unstable in the sup norm.

Read Full Post »

I’ve just uploaded this paper, with E. Grenier, on the arXiv (arXiv:1703.00881), entitled Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms, aiming a better understanding of the classical Prandtl’s boundary layers. Indeed, one of the key difficulties in dealing with boundary layers is the creation of (unbounded) vorticity in the inviscid limit.

(more…)

Read Full Post »

I’ve just submitted this new paper with E. Grenier (ENS de Lyon) on arxiv (scheduled to announce next Tuesday 1:00GMT), in which we construct the Green function for the classical Orr-Sommerfeld equations and derive sharp semigroup bounds for linearized Navier-Stokes equations around a boundary layer profile. This is part of the long program to understand the stability of classical Prandtl’s layers appearing in the inviscid limit of incompressible Navier-Stokes flows.

(more…)

Read Full Post »