Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion Academic Article

abstract

• 2016 Wiley Periodicals, Inc. In this paper, we consider the initial boundary value problem of the three-dimensional primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal diffusion in the temperature equation. Global well-posedness of the strong solution is established for any H2 initial data. An N-dimensional logarithmic Sobolev embedding inequality, which bounds the L-norm in terms of the Lq-norms up to a logarithm of the Lp-norm for p > N of the first-order derivatives, and a system version of the classic Grnwall inequality are exploited to establish the required a~priori H2 estimates for global regularity. 2016 Wiley Periodicals, Inc.

authors

• Titi, Edriss

published proceedings

• COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

author list (cited authors)

• Cao, C., Li, J., & Titi, E. S.

citation count

• 53

complete list of authors

• Cao, Chongsheng||Li, Jinkai||Titi, Edriss S

publication date

• August 2016

publisher

• Wiley  Publisher

published in

• Communications on Pure and Applied Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics

Digital Object Identifier (DOI)

• 10.1002/cpa.21576

start page

• 1492

end page

• 1531

volume

• 69

issue

• 8

URL

• http%3A%2F%2Fdx.doi.org%2F10.1002%2Fcpa.21576