摘要
The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard equation.When there is an inertial term,the equation becomes a parabolic-hyperbolic one.To overcome the difficulties from large perturbation and the hyperbolicity,a few elaborate energy estimates should be given,which are based on choosing suitable space of the smooth solution,even some inequalites in negative Sobolev space.More precisely,for 1-dimensional(1D)non-viscous case and 1D,2D,and 3D viscous case,the global existence of the smooth solutions are given.Moreover,several blow-up results are established by using the convex method.The results exhibit the interplay between the viscosity and the inertial term for the behavior of the smooth solution.
The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard equation. When there is an inertial term, the equation becomes a parabolic-hyperbolic one. To overcome the difficulties from large perturbation and the hyperbolicity, a few elaborate energy estimates should be given, which are based on choosing suitable space of the smooth solution, even some inequalites in negative Sobolev space. More precisely, for 1-dimensional(1D) non-viscous case and 1D, 2D, and 3D viscous case, the global existence of the smooth solutions are given. Moreover, several blow-up results are established by using the convex method. The results exhibit the interplay between the viscosity and the inertial term for the behavior of the smooth solution.
作者
丁蓉
吴志刚
DING Rong;WU Zhigang
基金
National Natural Science Foundation of China(No.11971100)
Fundamental Research Funds for the Central Universities,China(No.2232019D3-43)
