TY - JOUR
T1 - Global $H^2$-Regularity Results of the 3D Primitive Equations of the Ocean
AU - Y. He & J. Wu
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 452
EP - 477
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/537.html
KW - Primitive equations, ocean, regularity.
AB - <p style="text-align: justify;">In this article, we consider the 3D viscous primitive equations (PEs for brevity) of the ocean under two physically relevant boundary conditions for the $H^1$ and $H^2$ smooth initial data,
respectively. The $H^2$ regularity result of the solution for the viscous PEs of the ocean has been
unknown since the work by Cao and Titi [3], and Kobelkov [26]. In this article we provide the
global $H^2$-regularity results of the solution and its time derivatives for the 3D viscous primitive
equations of the ocean by using the $L^6$ estimates developed in [3] and some new energy estimate
techniques.</p>