Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

The SAR11 Group of Alpha-Proteobacteria Is Not Related to the Origin of Mitochondria

Although free living, members of the successful SAR11 group of marine alpha-proteobacteria contain a very small and A+T rich genome, two features that are typical of mitochondria and related obligate intracellular parasites such as the Rickettsiales. Previous phylogenetic analyses have suggested that Candidatus Pelagibacter ubique, the first cultured member of this group, is related to the Rickettsiales+mitochondria clade whereas others disagree with this conclusion. In order to determine the evolutionary position of the SAR11 group and its relationship to the origin of mitochondria, we have performed phylogenetic analyses on the concatenation of 24 proteins from 5 mitochondria and 71 proteobacteria. Our results support that SAR11 group is not the sistergroup of the Rickettsiales+mitochondria clade and confirm that the position of this group in the alpha-proteobacterial tree is strongly affected by tree reconstruction artefacts due to compositional bias. As a consequence, genome reduction and bias toward a high A+T content may have evolved independently in the SAR11 species, which points to a different direction in the quest for the closest relatives to mitochondria and Rickettsiales. In addition, our analyses raise doubts about the monophyly of the newly proposed Pelagibacteraceae family