- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 240387, 9 pages
The Inviscid Limit Behavior for Smooth Solutions of the Boussinesq System
College of Mathematics, Physics and Information Engineering, Jiaxing University, Zhejiang 314001, China
Received 13 January 2013; Accepted 30 March 2013
Academic Editor: Jesús I. Díaz
Copyright © 2013 Junlei Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Majda, Introduction to PDEs andWaves for the Atmosphere and Ocean, vol. 9 of Courant Lecture Notes in Mathematics, AMS/CIMS, 2003.
- J. Pedlosky, Geophysical Fluid Dynamics, Springer, New York, NY, USA, 1987.
- J. R. Cannon and E. DiBenedetto, “The initial value problem for the Boussinesq equations with data in ,” in Approximation Methods for Navier-Stokes Problems, vol. 771 of Lecture Notes in Mathematics, pp. 129–144, Springer, Berlin, Germany, 1980.
- D. Chae and H.-S. Nam, “Local existence and blow-up criterion for the Boussinesq equations,” Proceedings of the Royal Society of Edinburgh A, vol. 127, no. 5, pp. 935–946, 1997.
- D. Chae, “Global regularity for the 2D Boussinesq equations with partial viscosity terms,” Advances in Mathematics, vol. 203, no. 2, pp. 497–513, 2006.
- C. Foias, O. Manley, and R. Temam, “Attractors for the Bénard problem: existence and physical bounds on their fractal dimension,” Nonlinear Analysis. Theory, Methods & Applications, vol. 11, no. 8, pp. 939–967, 1987.
- B. Guo, “Spectral method for solving two-dimensional Newton-Boussinesq equations,” Acta Mathematicae Applicatae Sinica, vol. 5, pp. 27–50, 1989.
- B. Guo, “Nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations,” Chinese Annals of Mathematics B, vol. 16, no. 3, pp. 379–390, 1995.
- T. Y. Hou and C. Li, “Global well-posedness of the viscous Boussinesq equations,” Discrete and Continuous Dynamical Systems A, vol. 12, no. 1, pp. 1–12, 2005.
- Y. Taniuchi, “A note on the blow-up criterion for the inviscid 2-D Boussinesq equations,” in The Navier-Stokes Equations: Theory and Numerical Methods, vol. 223 of Lecture Notes in Pure and Applied Mathematics, pp. 131–140, Dekker, New York, NY, USA, 2002.
- P. Constantin, “Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations,” Communications in Mathematical Physics, vol. 104, no. 2, pp. 311–326, 1986.
- P. Constantin, “On the Euler equations of incompressible fluids,” American Mathematical Society, vol. 44, no. 4, pp. 603–621, 2007.
- A. Dutrifoy, “On 3-D vortex patches in bounded domains,” Communications in Partial Differential Equations, vol. 28, no. 7-8, pp. 1237–1263, 2003.
- T. Kato, “Nonstationary flows of viscous and ideal fluids in ,” vol. 9, pp. 296–305, 1972.
- N. Masmoudi, “Remarks about the inviscid limit of the Navier-Stokes system,” Communications in Mathematical Physics, vol. 270, no. 3, pp. 777–788, 2007.
- N. Masmoudi, “Examples of singular limits in hydrodynamics,” in Handbook of Differential Equations, pp. 195–275, North-Holland, Amsterdam, The Netherlands, 2007.
- H. S. G. Swann, “The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in ,” Transactions of the American Mathematical Society, vol. 157, pp. 373–397, 1971.
- R. R. Coifman and Y. Meyer, “Nonlinear harmonic analysis, operator theory and P.D.E,” in Beijing Lectures in Harmonic Analysis, vol. 112, pp. 3–45, Princeton University Press, Princeton, NJ, USA, 1986.
- T. Kato, “Liapunov functions and monotonicity in the Navier-Stokes equation,” in Functional-Analytic Methods for Partial Differential Equations, vol. 1450, pp. 53–63, Springer, Berlin, Germany, 1990.
- A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, vol. 27, Cambridge, UK, 2002.