Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 July 2020Accepted: 24 May 2021Published online: 16 September 2021Keywordsfluid dynamics, climate modeling, variational inequality, numerical analysis, conservation lawAMS Subject Headings35K86, 65K15, 76A20, 76D27, 76M12Publication DataISSN (print): 0036-1399ISSN (onli...

This paper studies the boundary layers that generally arise in approximations of the entropy discontinuous solutions to the initial-boundary value problem associated with a nonlinear hyperbolic system of conservation laws. We consider the vanishing viscosity method and several nite diierence schemes (Lax-Friedrichs type schemes, Godunov scheme). Assuming solely uniform L 1 bounds and for entrop...

Abstract. This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear ill-posedness results established by Gérard-Varet and Dormy [2], and an analysis in Guo and Tice [5]. We show that the asymptotic boundary-layer expansion ...

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Consider the initial value problem for the three dimensional Navier-Stokes equations with rotation in the half-space R+ subject to Dirichlet boundary conditions as well as the Ekman spiral which is a stationary solution to the above equations. It is proved that the Ekman spiral is nonlinearly stable with respect to L2-perturbations provided the corresponding Reynolds number is small enough. Mor...

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