UC Irvine

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 Grönwall inequality are exploited to establish the required a~priori H2 estimates for global regularity.© 2016 Wiley Periodicals, Inc.