Global well-posedness of the coupled atmosphere-ocean model of Lions, Temam and Wang

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Tim Binz, Princeton
Fine Hall 314

Joint work with F. Brandt, M. Hieber and T. Zöchling.

In their seminal articles [1,2] from 1993 Lions, Temam and Wang introduced a set of equations which describes the dynamics of the atmosphere and the ocean on a large scale. This model consists of two primitive equations coupled by non-linear wind-driven boundary conditions or non-linear traction conditions at the interface. 

In this talk we show the existence and uniqueness of global strong solutions to this problem.

Our proof rely on a new maximal $L^p$-regularity result for the hydrostatic Stokes operator with inhomogeneous boundary conditions, a Kato-Ponce type para-product inequality in Triebel-Lizorkin spaces due to Chae, and the splitting into barotropic and baroclinic modes for primitive equations discovered by Cao and Titi, as well as a careful analysis of the boundary coupling terms in each step. 

[1] J.L. Lions, R. Temam, Sh. H. Wang, Mathematical theory for the coupled atmosphere-ocean models (CAO III). J. Math. Pures Appl. 74 (1995), 105–163

[2] J.L. Lions, R. Temam, Sh. H. Wang, Models for the coupled atmosphere and ocean. (CAO I,II). Comput. Mech. Adv.1 (1993), 3–119