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Viscous Aubry-Mather theory and the Vlasov equation
On the existence and asymptotic stability of solutions for unsteady mixing-layer models
1. | Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Calle Tarfia, s/n, 41012, Sevilla, Spain, Spain, Spain |
References:
[1] |
A.-C. Bennis, T. Chacón-Rebollo, M. Gómez Mármol and R. Lewandowski, Numerical modelling of algebraic closure models of oceanic turbulent mixing layers, M2AN Math. Model. Numer. Anal., 44 (2010), 1255-1277.
doi: 10.1051/m2an/2010025. |
[2] |
A.-C. Bennis, T. Chacón-Rebollo, M. Gómez Mármol and R. Lewandowski, Stability of some turbulent vertical models for the ocean mixing boundary layer, Appl. Math. Lett., 21 (2008), 128-133.
doi: 10.1016/j.aml.2007.02.016. |
[3] |
H. Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations," Universitext, Springer, New York, 2011.
doi: 10.1007/978-0-387-70914-7. |
[4] |
T. Chacón-Rebollo, M. Gómez Mármol and S. Rubino, Analysis of numerical stability of algebraic oceanic turbulent mixing layer models, submitted to Appl. Math. Model., (2013). |
[5] |
S. N. Chow and J. K. Hale, "Methods of Bifurcation Theory," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], 251, Springer-Verlag, New York-Berlin, 1982.
doi: 10.1007/978-1-4613-8159-4. |
[6] |
A. Defant, Schichtung und zirkulation des atlantischen ozeans, (German) Wiss. Ergebn.: Deutsch. Atlant. Exp. Forsch., 6 (1936), 289-411. |
[7] |
L. C. Evans, "Partial Differential Equations," $2^{nd}$ edition, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. |
[8] |
P. R. Gent, The heat budget of the TOGA-COARE domain in an ocean model, J. Geophys. Res., 96 (1991), 3323-3330.
doi: 10.1029/90JC01677. |
[9] |
H. Goosse, E. Deleersnijder, T. Fichefet and M. H. England, Sensitivity of a global coupled ocean-sea ice model to the parameterization of vertical mixing, J. Geophys. Res., 104 (1999), 13681-13695.
doi: 10.1029/1999JC900099. |
[10] |
Z. Kowalik and T. S. Murty, "Numerical Modeling of Ocean Dynamics," Advanced Series on Ocean Engineering, Vol. 5, World Scientific, Singapore, 1993.
doi: 10.1142/1970. |
[11] |
O. A. Ladyženskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasi-Linear Equations of Parabolic Type," Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1968. |
[12] |
M. Lesieur, "Turbulence in Fluids," $3^{rd}$ edition, Fluid Mechanics and its Applications, 40, Kluwer Academic Publishers Group, Dordrecht, 1997.
doi: 10.1007/978-94-010-9018-6. |
[13] |
R. Lewandowski, "Analyse Mathématique et Océanographie," (French) Masson, Paris, 1997. |
[14] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," (French) Dunod; Gauthier-Villars, Paris, 1969. |
[15] |
R. C. Pacanowski and S. G. H. Philander, Parametrization of vertical mixing in numerical models of the tropical oceans, J. Phys. Oceanogr., 11 (1981), 1443-1451. Available from: http://journals.ametsoc.org/loi/phoc. |
[16] |
J. Pedloski, "Geophysical Fluid Dynamics," $2^{nd}$ edition, Springer-Verlag, New York-Berlin, 1987. |
[17] |
S. Rubino, Numerical modelling of oceanic turbulent mixing layers considering pressure gradient effects, in "Mascot10 Proceedings: IMACS Series in Comp. and Appl. Math." (eds. F. Pistella and R. M. Spitaleri), 16 (2011), 229-238. |
[18] |
R. Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comp., 62 (1994), 445-475.
doi: 10.2307/2153518. |
[19] |
J. Vialard and P. Delecluse, An ogcm study for the TOGA decade. Part I: Role of salinity in the physics of the western Pacific fresh pool, J. Phys. Oceanogr., 28 (1998), 1071-1088. Available from: http://journals.ametsoc.org/loi/phoc. |
show all references
References:
[1] |
A.-C. Bennis, T. Chacón-Rebollo, M. Gómez Mármol and R. Lewandowski, Numerical modelling of algebraic closure models of oceanic turbulent mixing layers, M2AN Math. Model. Numer. Anal., 44 (2010), 1255-1277.
doi: 10.1051/m2an/2010025. |
[2] |
A.-C. Bennis, T. Chacón-Rebollo, M. Gómez Mármol and R. Lewandowski, Stability of some turbulent vertical models for the ocean mixing boundary layer, Appl. Math. Lett., 21 (2008), 128-133.
doi: 10.1016/j.aml.2007.02.016. |
[3] |
H. Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations," Universitext, Springer, New York, 2011.
doi: 10.1007/978-0-387-70914-7. |
[4] |
T. Chacón-Rebollo, M. Gómez Mármol and S. Rubino, Analysis of numerical stability of algebraic oceanic turbulent mixing layer models, submitted to Appl. Math. Model., (2013). |
[5] |
S. N. Chow and J. K. Hale, "Methods of Bifurcation Theory," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], 251, Springer-Verlag, New York-Berlin, 1982.
doi: 10.1007/978-1-4613-8159-4. |
[6] |
A. Defant, Schichtung und zirkulation des atlantischen ozeans, (German) Wiss. Ergebn.: Deutsch. Atlant. Exp. Forsch., 6 (1936), 289-411. |
[7] |
L. C. Evans, "Partial Differential Equations," $2^{nd}$ edition, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. |
[8] |
P. R. Gent, The heat budget of the TOGA-COARE domain in an ocean model, J. Geophys. Res., 96 (1991), 3323-3330.
doi: 10.1029/90JC01677. |
[9] |
H. Goosse, E. Deleersnijder, T. Fichefet and M. H. England, Sensitivity of a global coupled ocean-sea ice model to the parameterization of vertical mixing, J. Geophys. Res., 104 (1999), 13681-13695.
doi: 10.1029/1999JC900099. |
[10] |
Z. Kowalik and T. S. Murty, "Numerical Modeling of Ocean Dynamics," Advanced Series on Ocean Engineering, Vol. 5, World Scientific, Singapore, 1993.
doi: 10.1142/1970. |
[11] |
O. A. Ladyženskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasi-Linear Equations of Parabolic Type," Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1968. |
[12] |
M. Lesieur, "Turbulence in Fluids," $3^{rd}$ edition, Fluid Mechanics and its Applications, 40, Kluwer Academic Publishers Group, Dordrecht, 1997.
doi: 10.1007/978-94-010-9018-6. |
[13] |
R. Lewandowski, "Analyse Mathématique et Océanographie," (French) Masson, Paris, 1997. |
[14] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," (French) Dunod; Gauthier-Villars, Paris, 1969. |
[15] |
R. C. Pacanowski and S. G. H. Philander, Parametrization of vertical mixing in numerical models of the tropical oceans, J. Phys. Oceanogr., 11 (1981), 1443-1451. Available from: http://journals.ametsoc.org/loi/phoc. |
[16] |
J. Pedloski, "Geophysical Fluid Dynamics," $2^{nd}$ edition, Springer-Verlag, New York-Berlin, 1987. |
[17] |
S. Rubino, Numerical modelling of oceanic turbulent mixing layers considering pressure gradient effects, in "Mascot10 Proceedings: IMACS Series in Comp. and Appl. Math." (eds. F. Pistella and R. M. Spitaleri), 16 (2011), 229-238. |
[18] |
R. Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comp., 62 (1994), 445-475.
doi: 10.2307/2153518. |
[19] |
J. Vialard and P. Delecluse, An ogcm study for the TOGA decade. Part I: Role of salinity in the physics of the western Pacific fresh pool, J. Phys. Oceanogr., 28 (1998), 1071-1088. Available from: http://journals.ametsoc.org/loi/phoc. |
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