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On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity

 

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Opened Access On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
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Author: Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2005-07
Published in: Applied Mathematics Letters, 18(7), 783-789
Document type: Article
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 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.
Cite: 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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URI: http://hdl.handle.net/11441/40293

DOI: 10.1016/j.aml.2004.07.024

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