Abstract
In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.
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References
Cannone, M., Chapter 3 Harmonic analysis tools for solving the incompressible Navier-Stokes equations, Handbook of Mathematical Fluid Dynamics, Vol. III, North-Holland, Amsterdam, 2004, 161–244.
Cannone, M., Meyer, Y. and Planchon, F., Solutions auto-similaries des équations de Navier-Stokes, Séminaire sur les Equations aux Dérivées Partielles, 1993–1994, Exp. No. VIII, 12 pages, Ecole Polytech., Palaiseau, 1994.
Chemin, J. Y. and Gallagher, I., Large, global solutions to the Navier-Stokes equations, slowly varying in one direction, Trans. Amer. Math. Soc., 362(6), 2010, 2859–2873.
Chemin, J. Y., Gallagher, I. and Paicu, M., Global regularity for some classes of large solutions to the Navier-Stokes equations, Ann. of Math., 173, 2011, 983–1012.
Chemin, J. Y., Paicu, M. and Zhang, P., Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable, J. Differential Equations, 256(1), 2014, 223–252.
Chemin, J. Y. and Zhang, P., On the global well-posedness to the 3-D incompressible anisotropic Navier- Stokes equations, Comm. Math. Phys., 272(2), 2007, 529–566.
Clay mathematics institute, Millennium prize problems, http://www.claymath.org/millenniumproblems/navier%E2%80%93stokes-equation
Fujita, H. and Kato, T., On the Navier-Stokes initial value problem, I, Arch. Ration. Mech. Anal., 16, 1964, 269–315.
Giga, Y. and Miyakama, T., Solutions in L r of the Navier-Stokes initial value problem, Arch. Ration. Mech. Anal., 89(3), 1985, 267–281.
Kato, T., Strong L p-solutions of the Navier-Stokes equations in Rm with applications to weak solutions, Math. Z., 187(4), 1984, 471–480.
Koch, H. and Tataru, D., Well-posedness for the Navier-Stokes equations, Adv. Math., 157(1), 2001, 22–35.
Leray, J., Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math., 63, 1934, 193–248.
Weissler, F. B., The Navier-Stokes initial value problem in L p, Arch. Ration. Mech. Anal., 74, 1980, 219–230.
Acknowledgement
The authors would like to express their gratitude to Professor Ta- Tsien Li for his helpful advice.
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This work was supported by the National Natural Science Foundation of China (Nos. 11471215, 11031001, 11121101, 11626156), Shanghai Leading Academic Discipline Project (No. XTKX2012), the Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), the Ministry of Education of China, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University and 111 Program of MOE, China (No. B08018).
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Peng, W., Zhou, Y. Global well-posedness of incompressible Navier-Stokes equations with two slow variables. Chin. Ann. Math. Ser. B 38, 787–794 (2017). https://doi.org/10.1007/s11401-017-1095-4
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DOI: https://doi.org/10.1007/s11401-017-1095-4