91 citations · 143 across the 14 of their papers we have counts for
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On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows
Emmanuel Grenier, Toan T. Nguyen
In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to . His An…
Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
Emmanuel Grenier, Toan T. Nguyen
This is a continuation and completion of the program (initiated in \cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linear…
Sublayer of Prandtl boundary layers
Emmanuel Grenier, Toan T. Nguyen
The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: . In \cite{Grenier}, one of the authors proved that there…
Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile
Emmanuel Grenier, Toan T. Nguyen
In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half plane and in the half spac…
Green function of Orr Sommerfeld equations away from critical layers
Emmanuel Grenier, Toan T. Nguyen
The classical Orr-Sommerfeld equations are the resolvent equations of the linearized Navier Stokes equations around a stationary shear layer profile in the half plane. In this pape…