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

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.

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