Abstract
The two-phase free boundary value problem for the isothermal Navier–Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and boundary contacts. It is shown that the problem is well-posed in an $$L_p$$ -setting, and that it generates a local semiflow on the induced state manifold. If the phases are connected, the set of equilibria of the system forms a $$(n+1)$$ -dimensional manifold, each equilibrium is stable, and it is shown that global solutions which do not develop singularities converge to an equilibrium as time goes to infinity. The latter is proved by means of the energy functional combined with the generalized principle of linearized stability.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
