References
- Cordoba D, Fefferman C, De LaLlave R. On squirt singularities in hydrodynamics. SIAM J Math Anal. 2004;36:204–213. doi: 10.1137/S0036141003424095
- Majda A. Introduction to PDEs and waves for the atmosphere and ocean. Vol. 9. New York: New York University, Courant Institute of Mathematical Sciences; Providence (RI): American Mathematical Society; 2003. (Courant Lecture Notes in Mathematics).
- Moffatt HK. Some remarks on topological fluid mechanics. In: Ricca RL, editor. An introduction to the geometry and topology of fluid flows. Dordrecht: Kluwer Academic Publishers; 2001. p. 3–10.
- Pedlosky J. Geophysical fluid dynamics. New York (NY): Springer-Verlag; 1987.
- Bodenschatz E, Pesch W, Ahlers G. Recent developments in Rayleigh-Bénard convection. Annu Rev Fluid Mech Annu Rev Palo Alto Calif. 2000;32:709–778. doi: 10.1146/annurev.fluid.32.1.709
- Busse FH. Fundamentals of thermal convection. In: Peltier WR, editor. Mantle convection: plate tectonics and global dynamics. The fluid mechanics of astrophysics and geophysics. Vol. 4. New York: Gordon and Breach; 1989. p. 23–95.
- Getling AV. Rayleigh-Bénard convection: structures and dynamics 11. River Edge (NJ): World Scientific; 1998. (Advanced Series in Nonlinear Dynamics).
- Lions JL. Perturbations singuliéres dans les problémes aux limites et en contrôle optimal 323. New York (NY): Springer-Verlag;1973. (Lecture Notes in Mathematics).
- Tritton DJ. Physical fluid dynamics. 2nd ed. New York: Oxford Science Publication, Clarendon, Oxford University Press, 1988.
- Constantin P, Foias C. Navier-Stokes equations. Chicago: University of Chicago Press; 1988.
- Wang XM. Infinite Prandtl number limit of Rayleigh-Bénard convection. Comm Pure Appl Math. 2004;LVII:1265–1282. doi: 10.1002/cpa.3047
- Wang XM. Large Prandtl number limit of the Boussinesq system of Rayleigh-Bénard convection. Appl Math Lett. 2004;17:821–825. doi: 10.1016/j.aml.2004.06.012
- Shi JG, Wang K, Wang S. The initial layer problem and infinite Prandtl number limit of Rayleigh-Bénard convection. Commun Math Sci. 2007;5(1):53–66. doi: 10.4310/CMS.2007.v5.n1.a2
- Foias C, Manley O, Rosa R, et al. Navier-Stokes equations and turbulence. Encyclopedia of mathematics and its applications, 83. Cambridge: Cambridge University Press; 2001.
- Grenier E, Masmoudi N. Ekman layers of rotating fluids, the case of well prepared initial data. Comm Partial Differ Equ. 1997;22:953–975. doi: 10.1080/03605309708821290
- Jiang S, Zhang JW, Zhao JN. Boundary-layer effects for the 2-D Boussinesq equations with vanishing diffusivity limit in the half plane. J Differ Equ. 2011;250:3907–3936. doi: 10.1016/j.jde.2011.01.002
- Kelliher JP, Temam R, Wang X. Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media. Phys D. 2011;240:619–628. doi: 10.1016/j.physd.2010.11.012
- Mazzucato A, Niu DJ, Wang XM. Boundary layer associated with a class of 3D nonlinear plane parallel channel flows. Indiana Univ Math J. 2011;60:1113–1136. doi: 10.1512/iumj.2011.60.4479
- Masmoudi N. The Euler limit of the Navier-Stokes equations and rotating fluids with boundary. Arch Rational Mech Anal. 1998;142(4):375–394. doi: 10.1007/s002050050097
- Mazzucato A, Taylor M. Vanishing viscosity plane parallel channel flow and related singular perturbation problems. Anal PDE. 2008;1(1):35–93. doi: 10.2140/apde.2008.1.35
- Oleinik OA, Samokhin VN. Mathematical models in boundary layer. London: Chapman and Hall; 1999.
- Schlichting H, Gersten K. Boundary-layer theory. Berlin: Springer Press; 2000.
- Temam R, Wang X. Boundary layer associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. J Differ Equ. 2002;179:647–686. doi: 10.1006/jdeq.2001.4038
- Wang X. Examples of boundary layers associated with the incompressible Navier-Stokes equations. Chin Ann Math Ser B. 2010;31(5):781–792. doi: 10.1007/s11401-010-0597-0
- Weinan E. Boundary layer theory and the zero viscosity limit of the Navier-Stokes equations. Acta Math Sin (Engl Ser). 2000;16:207–218. doi: 10.1007/s101140000034
- Cousteix J, Mauss J. Asymptotic analysis and boundary layers. Berlin: Springer; 2007.
- Holmes MH. Introduction to perturbation methods. New York (NY): Springer; 1995.
- Foias C, Manley O, Temam R. Attractors for the Bénard problem: existence and physical bounds on their fractal dimension. Nonlinear Anal TMA. 1987;11:939–967. doi: 10.1016/0362-546X(87)90061-7
- Gill AE. Atmosphere-ocean dynamics. San Diego (CA): Academic Press; 1982. (International Geophysics Series).
- Ly HV, Titi ES. Global Gevrey regularity for the Bénard convection in a porous medium with zero Darcy-Prandtl number. J Nonlinear Sci. 1999;9:333–362. doi: 10.1007/s003329900073
- Lu M, Wang Q. Regularity to Boussinesq equations with partial viscosity and large data in three-dimensional periodic thin domain. Nonlinear Anal. 2017;164:27–37. doi: 10.1016/j.na.2017.08.004
- Majda AJ, Bertozzi AL. Vorticity and incompressible flow 27. Cambridge: Cambridge University Press; 2002. (Cambridge Texts in Applied Mathematics).
- Klainerman S, Majda A. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm Pure Appl Math. 1981;34:481–524. doi: 10.1002/cpa.3160340405
- Ladyzhenskaya OA. The mathematical theory of Viscous incompressible flows. London: Gordon and Breach; 1969.
- Xin ZP. Viscous boundary layers and their stability. I J Part Diff Eqs. 1998;11:97–124.
- Evans LC. Partial differential equations. Vol. 19. Providence (RI): Graduate Studies in Mathematics, American Mathematical Society; 1998.
- Temam R. Navier-Stokes equations, theory and numerical analysis, reprint of the 1984 edition. Providence (RI): AMS Chelsea; 2001.