| 摘要: |
| 基于三维趋化系统弱解的整体存在性的结果,进一步考虑了一类带有 logistic 源抛物-抛物型趋 化方程组在三维情形时对应的齐次诺依曼初边值条件下弱解的最终光滑性;通过构造能量泛函并利用 Sobolev 最大正则性理论、Sobolev嵌入定理、Gagliardo-Nirenberg不等式、Young 不等式、 H?lder 不等式、Poincaré不等式、紧嵌入定理以及 Gronwall 不等式得到解的高阶正则性估计;结果表明:对于任意非负且适 当的初始值,可以证明到系统的弱解在一定的等待时间后变成经典解。 |
| 关键词: logistic源 趋化系统 能量泛函 最终光滑性 |
| DOI： |
| 分类号: |
| 基金项目: |
|
| The Final Smoothness of the Weak Solution of the Three-dimensional Chemotaxis System with Logistic Source |
|
JIANG Yong-feng
|
|
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
|
| Abstract: |
| Based on the results of the global existence of weak solutions of three-dimensional chemotaxis system, this paper further considers the final smoothness of the weak solutions of a class of parabolic chemotaxis equations with logistic source under the corresponding homogeneous Neumann initial boundary value conditions in three-dimensional case. In this paper, the higher-order regularity estimation of the solution is obtained by constructing the energy functional and using Sobolev maximum regularity theory, Sobolev embedding theorem, Gagliardo Nirenberg inequality, Young inequality, H?lder inequality, Poincaré inequality, compact embedding theorem and Gronwall inequality. The results show that for any nonnegative and appropriate initial value, it can be proved that the weak solution of the system becomes a classical solution after a certain waiting time. |
| Key words: logistic source chemotaxis system energy functional final smoothness |
