A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simul...A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.展开更多
Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the z...Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.展开更多
基金supported in part by the NSF Grant DMS 0906440 and DMS 1206438Fund of Indiana Universitysupported by the National Science Council of Taiwan under research grants NSC-100-2115-M-009-009-MY2.
文摘A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.
基金supported by the ANR (No. ANR-06-BLAN0306-01)the National Science Foundation (No.NSF-DMS-0906440) and the Research Fund of Indiana University
文摘Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.
