Abstract
We establish the vanishing viscosity limit of the zero-mode of the linearized Primitive Equations in a cube. Our method is based on the explicit construction and estimates of the boundary layers. This result, together with that in[12,15], allows us to conclude the vanishing viscosity limit of the linearized Primitive Equations in a cube.
Highlights
In this article, we are interested in the study of the mode-zero case of the LinearizedPrimitive Equations (LPEs) at small viscosity in a rectangle Ω = {(x, y) : 0 ≤ x ≤L1, 0 ≤ y ≤ L2}
Combining the convergence result proved in Theorem 1.1 with those established in [12, 15], we obtain the following vanishing viscosity limit for the linearized PEs system (1.15) in a cube
We avoid the construction of corner boundary layers entirely by taking advantage of the explicit construction and estimates of the parabolic boundary layers and ordinary boundary layers
Summary
We are interested in the study of the mode-zero case of the Linearized. A natural way of justifying these choices of local boundary conditions for the inviscid LPEs is to prove the vanishing viscosity limit, ideally with explicit convergence rates. The result of vanishing viscosity limit for the supercritical modes and subcritical modes are established in [15] and [12], respectively, by the careful study of various boundary layers. Combining the convergence result proved in Theorem 1.1 with those established in [12, 15], we obtain the following vanishing viscosity limit for the linearized PEs system (1.15) in a cube. We avoid the construction of corner boundary layers entirely by taking advantage of the explicit construction and estimates of the parabolic boundary layers and ordinary boundary layers This approach allows us to establish the vanishing viscosity limit. This work dealing with a subject dear to Claude-Michel Brauner (singular perturbations, see e.g. [1,2,3,4]) is dedicated to him with appreciation and friendship on the occasion of his seventieth birthday
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
