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Solutions faibles d’énergie infinie pour les équations de Navier–Stokes dans R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R} ^{3}$$\end{document}C. R. l’Acad. Sci. Ser. I Math., 328
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We study the so-called homogeneous model of wind-driven ocean circulation or the 2D quasigeostrophic model. Our attention focuses on performing a complete asymptotic analysis that highlights boundary layer formation along the coastal line. We assume rough coasts without any particular structure, resulting in the study of a nonlinear PDE system for the western boundary layer in an infinite domain. As a consequence, we look for the solution in nonlocalized Sobolev spaces. Under this hypothesis, the eastern boundary layer exhibits a singular behavior at low frequencies far from the rough boundary, leading to issues with convergence. The problem is tackled by imposing ergodicity properties. We establish the well-posedness of the governing boundary layer equations and the asymptotic solution. Our results generalize the ones in Bresch and Gérard-Varet (Commun Math Phys 253(1):81–119, 2005) for periodic irregularities.
Archive for Rational Mechanics and Analysis – Springer Journals
Published: Jun 1, 2023
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