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Volume 11, Issue 3
Global $H^2$-Regularity Results of the 3D Primitive Equations of the Ocean

Y. He & J. Wu

Int. J. Numer. Anal. Mod., 11 (2014), pp. 452-477.

Published online: 2014-11

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  • Abstract

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.

  • Keywords

Primitive equations, ocean, regularity.

  • AMS Subject Headings

35B41, 35Q35, 37L, 65M70, 86A10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-11-452, author = {Y. He and J. Wu}, title = {Global $H^2$-Regularity Results of the 3D Primitive Equations of the Ocean}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {452--477}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/537.html} }
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 -

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.

Y. He and J. Wu. (2014). Global $H^2$-Regularity Results of the 3D Primitive Equations of the Ocean. International Journal of Numerical Analysis and Modeling. 11 (3). 452-477. doi:
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