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Uniqueness of solution for the 2D Primitive Equations with friction condition on the bottom

 

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Opened Access Uniqueness of solution for the 2D Primitive Equations with friction condition on the bottom
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Author: Bresch, Didier
Guillén González, Francisco Manuel
Masmoudi, Nader
Rodríguez Bellido, María Ángeles
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2001
Published in: VII Jornadas Zaragoza-Pau de Matemática Aplicada y Estadística, 2001, Jaca (Huesca, España), 135-143
Document type: Presentation
Abstract: Uniqueness of solution for the Primitive Equations with Dirichlet conditions on the bottom is an open problem even in 2D domains. In this work we prove a result of additional regularity for a weak solution v for the Primitive Equations when we replace Dirichlet boundary conditions by friction conditions. This allows to obtain uniqueness of weak solution global in time, for such a system [3]. Indeed, we show weak regularity for the vertical derivative of the solution, ∂zv for all time. This is because this derivative verifies a linear pde of convection-diffusion type with convection velocity v, and the pressure belongs to a L 2 -space in time with values in a weighted space.
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URI: http://hdl.handle.net/11441/26764

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