Regularity results for the stationary primitive equations of the atmosphere and the ocean. (English) Zbl 0863.35085
The purpose of this paper is to establish the regularity of weak solutions of the stationary primitive equations. First, the primitive equations (especially the large scale equations of the ocean) are introduced. Then, the regularity results for systems of elliptic equations in domains with corners and with nonhomogeneous boundary conditions are established. Finally, the regularity of solutions of the linearized stationary large scale equations of the ocean, and the \(H^2\)-regularity of solutions of the linear primitive equations of the coupled system atmosphere-ocean is proved.
Reviewer: V.A.Sava (Iaşi)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
regularity in domains with corners; primitive equations of the atmosphere; large scale equations of the oceanReferences:
| [1] | Lions, J.-L.; Temam, R.; Wang, S., New formulations of the primitive equations of the atmosphere and applications,, Nonlinearity, 5, 237-288 (1992) · Zbl 0746.76019 |
| [2] | Lions, J.-L.; Temam, R.; Wang, S., On the equations of large-scale ocean,, Nonlinearity, 5, 1007-1053 (1992) · Zbl 0766.35039 |
| [3] | Lions, J.-L.; Temam, R.; Wang, S., Models of the coupled atmosphere and ocean (CAO I), (Oden, J. T., Computational Mechanics Advances, Vol. 1 (1993), Elsevier: Elsevier New York), 5-54 · Zbl 0805.76011 |
| [4] | LIONS J.-L., TEMAM R. & WANG S., Mathematical study of the coupled models of atmosphere and ocean (CAO III), J. Math. pures appl.; LIONS J.-L., TEMAM R. & WANG S., Mathematical study of the coupled models of atmosphere and ocean (CAO III), J. Math. pures appl. · Zbl 0866.76025 |
| [5] | Ziane, M. B., Regularity results for Stokes-type systems related to climatology,, Appl. Math. Lett., 8, 53-58 (1995) · Zbl 0830.35098 |
| [6] | ZIANE M.B., Regularity results for Stokes-type systems, Applic. Analysis; ZIANE M.B., Regularity results for Stokes-type systems, Applic. Analysis · Zbl 0837.35030 |
| [7] | Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions,, Communs pure appl. Math, 12, 623-723 (1959) · Zbl 0093.10401 |
| [8] | Temam, R., (Navier-Stokes Equations, 3rd revised edition, Studies in Mathematics and its Applications, Vol. 2 (1984), North-Holland: North-Holland Amsterdam) · Zbl 0572.35083 |
| [9] | Aubin, T., (Nonlinear Analysis on Manifolds, Monge-Ampere Equations. (1982), Springer: Springer Amsterdam) · Zbl 0512.53044 |
| [10] | Dauge, M., (Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Mathematics, 1341 (1988), Springer: Springer New York) · Zbl 0668.35001 |
| [11] | Dauge, M., Problèmes mixtes pour le Laplacien dans des domaines polyèdraux courbes, C.r. Acad. Sci. Paris, 309, 553-558 (1980) · Zbl 0715.35022 |
| [12] | GRISVARD P., Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics; GRISVARD P., Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics · Zbl 0695.35060 |
| [13] | Zolesio, J. L., Multiplication dans les espaces de Besov, Prov. R. Soc. Edinb. (1977) · Zbl 0382.46020 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
