caa a22 4500 445344733 CHVBK 20180317142825.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00233-010-9281-7 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9281-7 Asymptotic stability of finite energy in Navier Stokes-elastic wave interaction [Elektronische Daten] [Irena Lasiecka, Yongjin Lu] We consider a model of fluid-structure interaction in a bounded domain Ω∈ℝ2 where Ω is comprised of two open adjacent sub-domains occupied, respectively, by the solid and the fluid. This leads to a study of Navier Stokes equation coupled on the interface to the dynamic system of elasticity. The characteristic feature of this coupled model is that the resolvent is not compact and the energy function characterizing balance of the total energy is weakly degenerated. These combined with the lack of mechanical dissipation and intrinsic nonlinearity of the dynamics render the problem of asymptotic stability rather delicate. Indeed, the only source of dissipation is the viscosity effect propagated from the fluid via interface. It will be shown that under suitable geometric conditions imposed on the geometry of the interface, finite energy function associated with weak solutions converges to zero when the time t converges to infinity. The required geometric conditions result from the presence of the pressure acting upon the solid. Springer Science+Business Media, LLC, 2010 Asymptotic stability nationallicence Navier-Stokes-elastic interaction nationallicence Geometric conditions for stability nationallicence Finite energy nationallicence Lasiecka Irena Department of Mathematics, University of Virginia, 22904, Charlottesville, VA, USA aut Lu Yongjin Department of Mathematics, University of Virginia, 22904, Charlottesville, VA, USA aut Semigroup Forum Springer-Verlag 82/1(2011-02-01), 61-82 0037-1912 82:1<61 2011 82 233 https://doi.org/10.1007/s00233-010-9281-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9281-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lasiecka Irena Department of Mathematics, University of Virginia, 22904, Charlottesville, VA, USA aut NATIONALLICENCE 700 1- Lu Yongjin Department of Mathematics, University of Virginia, 22904, Charlottesville, VA, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/1(2011-02-01), 61-82 0037-1912 82:1<61 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer