On H² solutions and z-weak solutions of the 3D Primitive Equations

2015/07/23 by Ning Ju, Ju, Ning
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1507.06685

arXiv admin note: substantial text overlap with arXiv:1507.05992

arxiv created 2015/07/23 · openalex publication_date 2015/07/23 · arxiv updated 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Global in time well-posedness of H² solutions and z-weak solutions of the 3D Primitive equations in a bounded cylindrical domain is proved. More specifically, uniform in time boundedness and bounded absorbing sets are obtained for both H² solutions and z-weak solutions, as well as uniqueness of the z-weak solution for the 3D Primitive equations. The result for H² solutions improves a recent one proved in[6]. The result for z-weak solution positively resolves the problem of global existence and uniqueness of z-weak solutions of the 3D primitive equations, which has been open since the work of [14].

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