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Regularity results for Stokes type systems. (English) Zbl 0837.35030
The aim of this work is to study the regularity of solutions of Stokes type systems related to the large scale equations of the ocean and the primitive equations of the coupled system atmosphere-ocean, which have appeared in the work of J. L. Lions, R. Temam and S. Wang [Nonlinearity 5, 1007-1053 (1992; Zbl 0766.35039); ibid., 237-288 (1992; Zbl 0746.76019); and Comput. Mech. Adv. 1, No. 1, 55-119 (1993; Zbl 0805.76052)]. We prove various regularity results for strongly elliptic boundary value problems in cylinder-type domains with nonhomogeneous boundary conditions, as well as the $$H^2$$-regularity for the Stokes-type system built into these equations.

##### MSC:
 35D10 Regularity of generalized solutions of PDE (MSC2000) 35J65 Nonlinear boundary value problems for linear elliptic equations 35Q30 Navier-Stokes equations 76D07 Stokes and related (Oseen, etc.) flows 86A10 Meteorology and atmospheric physics
##### Keywords:
large scale equations of the ocean
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