Article
On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
Author/s | Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2005-07 |
Deposit Date | 2016-04-22 |
Published in |
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Abstract | In this note, we prove that given u a weak solution of the Primitive Equations, imposing an additional condition on the vertical derivative of the velocity u (concretely ∂zu ∈ L∞(0, T;L2(Ω)) ∩ L2(0, T; H1(Ω))), then two ... In this note, we prove that given u a weak solution of the Primitive Equations, imposing an additional condition on the vertical derivative of the velocity u (concretely ∂zu ∈ L∞(0, T;L2(Ω)) ∩ L2(0, T; H1(Ω))), then two different results hold; namely, uniqueness of weak solution (any weak solution associated to the same data that u must coincide with u) and global in time strong regularity for u (without “smallness assumptions” on the data). Both results are proved when either Dirichlet or Robin type conditions on the bottom are considered. In the last case, a domain with a strictly bounded from below depth has to be imposed, even for the uniqueness result. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | BFM2000-1317 |
Citation | Guillén González, F.M. y Rodríguez Bellido, M.Á. (2005). On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity. Applied Mathematics Letters, 18 (7), 783-789. |
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