Green function for linearized Navier–Stokes around a boundary shear layer profile for long wavelengths

  • Emmanuel Grenier

    École Normale Supérieure de Lyon, France
  • Toan T. Nguyen

    Pennsylvania State University, State College, USA
Green function for linearized Navier–Stokes around a boundary shear layer profile for long wavelengths cover
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Abstract

This paper is the continuation of a program, initiated in Grenier and Nguyen [SIAM J. Math. Anal. 51 (2019); J. Differential Equations 269 (2020)], to derive pointwise estimates on the Green function of Orr–Sommerfeld equations. In this paper we focus on long wavelength perturbations, more precisely horizontal wave numbers α\alpha of order ν1/4\nu^{1/4}, which correspond to the lower boundary of the instability area for monotonic profiles.

Cite this article

Emmanuel Grenier, Toan T. Nguyen, Green function for linearized Navier–Stokes around a boundary shear layer profile for long wavelengths. Ann. Inst. H. Poincaré Anal. Non Linéaire (2022),

DOI 10.4171/AIHPC/64