Addendum to “The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation”

Abstract

In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013) .Keywords: swimming models, coupled PDE/ODE systems, nonstationary Stokes equation.In our recent work (Khapalov, 2013) we introduced the following mathematical model for a swimmer whose body consists of finitely many subsequently connected parts S i (z i (t) linked by rotational and elastic Hooke forces:In the above, Ω is a bounded domain in R 3 with boundary ∂Ω of class C 2 , y(x, t) and p(x, t) are respectively the velocity and the pressure of the fluid at point x = (x 1 , x 2 , x 3 ) ∈ Ω at time t, while ν is the kinematic viscosity constant.The swimmer in (1)- (3) is modeled as a collection of n open connected bounded sets S i (z i (t)), i = 1, . . . , n, of non-zero measure, identified with the fluid within the space they occupy. The points z i (t) are their respective centers of mass. The sets S i (z i (t)) are viewed as the given sets S i (0) ("0" stands for the origin) that have been shifted to the respective positions z i (t) without changing their orientation in space. Respectively, for i = 1, . . . , n,Our goal in this addendum is to address the following unintentional omission in the description of the force term in (3). Namely, the forces described in this term are Unauthenticated Download Date | 5/13/18 2:18 AM