Abstract
Firstly, a priori estimates are obtained for the existence and uniqueness of solutions of two dimensional KDV equations, and prove the existence of the global attractor, finally get the upper bound estimation of the Hausdorff and fractal dimension of attractors.
Highlights
Studies on the infinite dimension system with high dimension have obtained many achievements in recent years, such as [1,2,3,4,5]
The authors study the estimates of global attractor for one-dimensional KDV equation and its dimension
This paper further studies the global attractor of twodimensional KDV equations and its upper bound estimation of the Hausdorff and fractal dimension of attractors
Summary
Studies on the infinite dimension system with high dimension have obtained many achievements in recent years, such as [1,2,3,4,5]. The authors study the estimates of global attractor for one-dimensional KDV equation and its dimension. This paper further studies the global attractor of twodimensional KDV equations and its upper bound estimation of the Hausdorff and fractal dimension of attractors. The following form 2D-KDV equation is studied in this paper ut uxxx u uv x. The rest of this paper is organized as follows. C denotes a positive constant whose value may change in different positions of chains of inequalities
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