Uniqueness of solution for the 2D primitive equations with friction condition on the bottom

Autores: D. Bresch, N. Masmoudix, María Angeles Rodríguez Bellido , Francisco Manuel Guillén González
Localización: VII Jornadas Zaragoza-Pau de Matemática Aplicada y estadística: Jaca (Huesca). 17-18 de septiembre de 2001 / coord. por Monique Madaune-Tort , 2003, ISBN 84-96214-04-4, págs. 135-144
Idioma: inglés
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Resumen
- 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 L2-space in time with values in a weighted space.