Presentation
Uniqueness of solution for the 2D Primitive Equations with friction condition on the bottom
Author/s | Bresch, Didier
Guillén González, Francisco Manuel Masmoudi, Nader Rodríguez Bellido, María Ángeles |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2001 |
Deposit Date | 2015-07-10 |
Published in |
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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 ... 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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