TY - JOUR
T1 - Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile
AU - Grenier, Emmanuel
AU - Nguyen, Toan T.
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/11/15
Y1 - 2020/11/15
N2 - 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 space (R+2 or R+3), with Dirichlet boundary conditions, assuming that this shear layer in spectrally unstable for Euler equations. In the inviscid limit, due to the prescribed no-slip boundary conditions, vorticity becomes unbounded near the boundary. The novelty of this paper is to introduce boundary layer norms that capture the unbounded vorticity and to derive sharp estimates on this vorticity that are uniform in the inviscid limit.
AB - 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 space (R+2 or R+3), with Dirichlet boundary conditions, assuming that this shear layer in spectrally unstable for Euler equations. In the inviscid limit, due to the prescribed no-slip boundary conditions, vorticity becomes unbounded near the boundary. The novelty of this paper is to introduce boundary layer norms that capture the unbounded vorticity and to derive sharp estimates on this vorticity that are uniform in the inviscid limit.
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U2 - 10.1016/j.jde.2020.06.046
DO - 10.1016/j.jde.2020.06.046
M3 - Article
AN - SCOPUS:85087302598
SN - 0022-0396
VL - 269
SP - 9384
EP - 9403
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 11
ER -