Inhaltszusammenfassung

In this paper the two-dimensional Navier–Stokes system for incompressible fluid coupled with a parabolic equation through the Neumann type boundary condition for the second component of the velocity is considered. Navier–Stokes equations are defined on a given time dependent domain. We prove the existence of a weak solution for this system. In addition, we prove the continuous dependence of solutions on the data for a regularized version of this system. For a special case of this regularized ...In this paper the two-dimensional Navier–Stokes system for incompressible fluid coupled with a parabolic equation through the Neumann type boundary condition for the second component of the velocity is considered. Navier–Stokes equations are defined on a given time dependent domain. We prove the existence of a weak solution for this system. In addition, we prove the continuous dependence of solutions on the data for a regularized version of this system. For a special case of this regularized system also a problem with an unknown interface is solved. The problem under consideration is an approximation of the fluid-structure interaction problem proposed by A. Quarteroni in [19]. We conjecture that our approach is useful also for the numerical treatment of the problem and at the end we shortly present our numerical experiments.» weiterlesen» einklappen

Schlüsselwörter

• Navier–Stokes equations, time dependent domain, fluid-structure interaction, Neumann boundary condition

Autoren

Klassifikation

DDC Sachgruppe:
Mathematik