Mathematics – Analysis of PDEs
Scientific paper
2004-07-21
Mathematics
Analysis of PDEs
72 pages, to appear in Archive for Rational Mechanics and Analysis
Scientific paper
10.1007/s00205-004-0340-7
The motion of an elastic solid inside of an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), when the elastic solid is the linear Kirchhoff elastic material. The solution is found using a topological fixed-point theorem that requires the analysis of a linear problem consisting of the coupling between the time-dependent Navier-Stokes equations set in Lagrangian variables and the linear equations of elastodynamics, for which we prove the existence of a unique weak solution. We then establish the regularity of the weak solution; this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases. Our functional framework is optimal, and provides the a priori estimates necessary for us to employ our fixed-point procedure.
Coutand Daniel
Shkoller Steve
No associations
LandOfFree
On the motion of an elastic solid inside of an incompressible viscous fluid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the motion of an elastic solid inside of an incompressible viscous fluid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the motion of an elastic solid inside of an incompressible viscous fluid will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1048