二维Newton-Boussinesq方程周期初值问题经典解的整体存在性

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基金项目: 国家自然科学基金资助项目(10871075;10926101);广东省自然科学基金资助项目(9451064201003736;9151064201000040)

Global Existence of Solutions of the Periodic Initial Value Problems for Two-Dimensional Newton-Boussinesq Equations

1.
Department of Mathematics, South China Agricultural University, Guangzhou 510642, P. R. China;

摘要: 研究一类二维Newton-Boussinesq方程的周期初值问题，将方程转化为积分方程，用不动点原理得到解的局部存在性，用能量估计的方法证明经典解的整体存在性．
- 非线性二维Newton-Boussinesq方程 /
- 经典解 /
- 先验估计
Abstract: A class of periodic initial value problems for two-dmiensional Newton-Bouss inesqequations was investigated.First the Newton-Boussinesq equations were turned into the equivalent integral equations,then by the iteration methods the local existence of the solutions was obtained.Finally using the method of a priori estimates,the global existence of the solutions was proved.
- nonlinear two-dimensional Newton-Boussinesq equations /
- classical solution /
- a priori estmiates

[1]	郭柏灵，黄海洋，蒋慕容.金兹堡-朗道方程[M].北京：科学出版社，2002.
[2]	郭柏灵.无穷维动力系统（上下册）[M]. 北京：国防工业出版社，2000.
[3]	GUO Bo-ling.Spectral method for solving two dimensional Newton-Boussinesq equations[J].Acta Mathematicac Applicatae Sinica，1989，5(3):208-218. doi: 10.1007/BF02006004
[4]	GUO Bo-ling.Nonlinear Galerkin methods for solving two dimensional Newton-Boussinesq equations[J].Chin Ann of Math, Ser B，1995，16(3):379-390.
[5]	Fucci G，WANG Bi-xing，Singh P.Asymptotic behavior of the Newton-Boussinesq equation in a two-dimensional channel[J].Nonlinear Analysis: Theory，Methods Applications，2009，70(5):2000-2013.
[6]	Temam R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].Berlin:Springer-Verlag，1988.