一类可压缩非牛顿流体弱解的吸收集问题  

An Absorbing Set for Weak Solutions of a Class of Non-Newtonian Compressible Fluids

作　　者：张思敏 郭闪闪 ZHANG Simin;GUO Shanshan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第5期91-98,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.12001074);重庆市教育委员会科学技术研究项目(No.KJQN202000536);重庆市科学技术局科学研究项目(No.cstc2020jcyj-msxmX0606);重庆师范大学(博士启动)基金项目(No.19XLB012)。

摘　　要：【目的】研究一类可压缩非牛顿流体在三维有界Lipschitz区域内的吸收集存在性问题。【方法】利用H9lder不等式、Sobolev嵌入定理,结合Gronwall引理等方法,得到精确的能量估计。【结果】首先根据有限能量弱解定义,给出能量E表达式,其次借助重整化解与有界算子B的辅助引理,得到衰减估计,进而得到能量的局部有界性,最后找出常数E_(∞),当t>T时,E[ρ,u](t)≤E_(∞) a.e.。【结论】在外力函数是有界可测的假设条件下,非牛顿流体方程组有限能量弱解的吸收集存在。[Purposes]The existence of absorbing set of weak solutions of a class of non-Newtonian compressible fluids was considered. [Methods]The precise energy estimates was established using H9 lder inequality、Sobolev embedding theorem and Gronwall lemma.[Findings]Firstly, the expression of energy E was given based on the definition of finite energy weak solution. Secondly, the decay estimates were obtained by auxiliary lemmas of the renormalized solution and the bounded liner operator B, moreover, the local bounded of energy was established. Finally, the constant E_(∞) was found such that E[ρ,u](t)≤E_(∞) a.e. when t>T.[Conclusions]Under the assumption that external force function was bounded and measurable, the absorbing set of weak solutions of non-Newtonian fluids was established.

关 键 词：可压缩流体 有限能量弱解 非牛顿流体 吸收集 

分 类 号：O175.29[理学—数学]