참고문헌
- R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- J. D. Avrin, Large-eigenvalue global existence and regularity results for the Navier-Stokes equations, J. Differential Equations 127 (1996), 365-390. https://doi.org/10.1006/jdeq.1996.0074
- P. Constantin and C. Foias, Navier-Stokes equations, University of Chicago Press, Chicago, 1988
- Lawrence C. Evans, Partial Differential Equations, American Mathematical Society, Rhode Island, 1998.
- H. Fujita and T. Kato, On the Navier-Stokes initial value problem, Arch. Rational Mech. Anal. 16 (1964), 269-315. https://doi.org/10.1007/BF00276188
- E. Hopf, Uber die Anfangswertaufgabe fur die hydrodynamischen Grudgleichungen, Math. Nachr. 4 (1951), 213-231.
- D. Iftimie and G. Raugel, Some results on the Navier-Stokes equations in thin 3D domains, J. Differential Equations. 169 (2001), 281-331. https://doi.org/10.1006/jdeq.2000.3900
- D. Iftimie, G. Raugel, and G. R. Sell, Navier-Stokes equations in thin 3D domains with Navier boundary conditions, Indiana Univ. Math. J. 56(3) (2007), 1083-1156. https://doi.org/10.1512/iumj.2007.56.2834
- H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch, Rational Mech. Anal. 16 (1964), 269-315. https://doi.org/10.1007/BF00276188
- I. Kukavica and M. Ziane, Regularity of the Navier-Stokes equation in a thin periodic domain with large data, Discrete and continuous dynamical system 18(1) (2006), 67-86.
- J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248. https://doi.org/10.1007/BF02547354
- G. Raugel and G. R. Sell, Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993), 503-568.
- G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Applied Math. Sciences 143, Springer, Berlin, 2002.
- G. Ponce, R. Racke, T.C. Sideris and E.S. Titi, Global Stability of Large Solutions to the 3D Navier-Stokes Equations, Commun. Math. Phys. 159 (1993), 329-341.
- R. Temam and M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Eqations. 1 (1996), 499-546.
- R. Temam, Navier-Stokes equations and nonlinear functional analysis, CBMS Regional Conference Series, No. 66, SIAM, Philadelphia, 1995.