On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
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 a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/40293 |
| Acceso en línea: | http://hdl.handle.net/11441/40293 https://doi.org/10.1016/j.aml.2004.07.024 |
| Access Level: | acceso abierto |
| Palabra clave: | Weak-strong uniqueness primitive equations anisotropic estimates strong solution |
| Sumario: | 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. |
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