Strong well-posedness for a class of dynamic outflow boundary conditions for incompressible Newtonian flows

Content Provider	Semantic Scholar
Author	Bothe, Dieter Kashiwabara, Takahito Köhne, Matthias
Copyright Year	2016
Abstract	Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier–Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the outlet. As a key building block for the analysis of such problems, we consider the Stokes equations with such dynamic outflow boundary conditions in a halfspace and prove the existence of a strong solution in the appropriate Sobolev–Slobodeckij setting with $${L_p}$$Lp (in time and space) as the base space for the momentum balance. For nonvanishing stress contribution in the boundary condition, the problem is actually shown to have $${L_p}$$Lp-maximal regularity under the natural compatibility conditions. Aiming at an existence theory for problems in weakly singular domains, where different boundary conditions apply on different parts of the boundary such that these surfaces meet orthogonally, we also consider the prototype domain of a wedge with opening angle $${\frac{\pi}{2}}$$π2 and different combinations of boundary conditions: Navier-Slip with Dirichlet and Navier-Slip with the dynamic outflow boundary condition. Again, maximal regularity of the problem is obtained in the appropriate functional analytic setting and with the natural compatibility conditions.
Starting Page	131
Ending Page	171
Page Count	41
File Format	PDF HTM / HTML
DOI	10.1007/s00028-016-0352-4
Alternate Webpage(s)	https://arxiv.org/pdf/1603.09220v1.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s00028-016-0352-4
Volume Number	17
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article