-
Previous Article
Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in $\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}$
- DCDS Home
- This Issue
-
Next Article
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. |
| [1] |
Zhi Lin, Katarína Boďová, Charles R. Doering. Models & measures of mixing & effective diffusion. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 259-274. doi: 10.3934/dcds.2010.28.259 |
| [2] |
Fabrizio Colombo, Irene Sabadini, Frank Sommen. The inverse Fueter mapping theorem. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1165-1181. doi: 10.3934/cpaa.2011.10.1165 |
| [3] |
Md. Ibrahim Kholil, Ziqi Sun. A uniqueness theorem for inverse problems in quasilinear anisotropic media. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022008 |
| [4] |
Qixuan Wang, Hans G. Othmer. The performance of discrete models of low reynolds number swimmers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1303-1320. doi: 10.3934/mbe.2015.12.1303 |
| [5] |
Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems and Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099 |
| [6] |
Laurent Imbert, Michael J. Jacobson, Jr., Arthur Schmidt. Fast ideal cubing in imaginary quadratic number and function fields. Advances in Mathematics of Communications, 2010, 4 (2) : 237-260. doi: 10.3934/amc.2010.4.237 |
| [7] |
Zhiming Chen, Chao Liang, Xueshuang Xiang. An anisotropic perfectly matched layer method for Helmholtz scattering problems with discontinuous wave number. Inverse Problems and Imaging, 2013, 7 (3) : 663-678. doi: 10.3934/ipi.2013.7.663 |
| [8] |
Raffaele Chiappinelli. Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem. Conference Publications, 2007, 2007 (Special) : 260-268. doi: 10.3934/proc.2007.2007.260 |
| [9] |
Qinghua Ma, Zuoliang Xu, Liping Wang. Recovery of the local volatility function using regularization and a gradient projection method. Journal of Industrial and Management Optimization, 2015, 11 (2) : 421-437. doi: 10.3934/jimo.2015.11.421 |
| [10] |
Yanfei Wang, Qinghua Ma. A gradient method for regularizing retrieval of aerosol particle size distribution function. Journal of Industrial and Management Optimization, 2009, 5 (1) : 115-126. doi: 10.3934/jimo.2009.5.115 |
| [11] |
Dariusz Idczak. A global implicit function theorem and its applications to functional equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2549-2556. doi: 10.3934/dcdsb.2014.19.2549 |
| [12] |
Ben Green, Terence Tao, Tamar Ziegler. An inverse theorem for the Gowers $U^{s+1}[N]$-norm. Electronic Research Announcements, 2011, 18: 69-90. doi: 10.3934/era.2011.18.69 |
| [13] |
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 |
| [14] |
Xiaoxue Gong, Ying Xu, Vinay Mahadeo, Tulin Kaman, Johan Larsson, James Glimm. Mesh convergence for turbulent combustion. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4383-4402. doi: 10.3934/dcds.2016.36.4383 |
| [15] |
Herbert Egger, Manuel Freiberger, Matthias Schlottbom. On forward and inverse models in fluorescence diffuse optical tomography. Inverse Problems and Imaging, 2010, 4 (3) : 411-427. doi: 10.3934/ipi.2010.4.411 |
| [16] |
Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems and Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81 |
| [17] |
Robert E. Beardmore, Rafael Peña-Miller. Antibiotic cycling versus mixing: The difficulty of using mathematical models to definitively quantify their relative merits. Mathematical Biosciences & Engineering, 2010, 7 (4) : 923-933. doi: 10.3934/mbe.2010.7.923 |
| [18] |
Juntao Sun, Tsung-fang Wu. The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3651-3682. doi: 10.3934/dcds.2021011 |
| [19] |
He Zhang, Haibo Chen. The effect of the weight function on the number of nodal solutions of the Kirchhoff-type equations in high dimensions. Communications on Pure and Applied Analysis, 2022, 21 (8) : 2701-2721. doi: 10.3934/cpaa.2022069 |
| [20] |
Colin J. Cotter, Michael John Priestley Cullen. Particle relabelling symmetries and Noether's theorem for vertical slice models. Journal of Geometric Mechanics, 2019, 11 (2) : 139-151. doi: 10.3934/jgm.2019007 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]