2022/04/01 by Haigang Li, Li, Haigang, Longjuan Xu +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2204.00254
openalex publication_date 2022/04/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
It is vital important in material sciences and fluid mechanics to study the field enhancements in the narrow region between two inclusions. Complex fluids including particle suspensions usually result in complicated flow behavior. In this paper we establish the pointwise upper bounds of the gradient and the second-order partial derivatives for the Stokes flow when two rigid particles are closely spaced suspending in an open bounded domain and away from the boundary in dimension two. Moreover, the lower bounds of the gradient estimates at the narrowest place of the neck region show the optimality of the blow-up rate. These results are valid for inclusions with arbitrary shape.