A stream‐function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
Copyright policy )A stream‐function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
AbstractIn this paper we derive a mixed variational formulation for the exterior Stokes problem in terms of the vorticity and stream function, or the vector potential in three dimensions. The main steps are the construction of the stream function (or vector potential) and the proof of the Babuška–Brezzi ‘inf‐sup’ condition. The two‐ and three‐dimensional cases are treated separately because the structure of the stream function differs substantially according to the number of dimensions considered. The conclusion of this work is that if the problem is set in the weighted Sobolev spaces of Hanouzet and Giroire, the analysis of the exterior Stokes problem is quite the same as if the domain were bounded.
- Sorbonne University France
- University of Lisbon Portugal
- Sorbonne Paris Cité France
- University of Nantes France
- University of Nantes France
weak variational formulation, Variational methods for second-order elliptic equations, Variational methods applied to problems in fluid mechanics, Existence of generalized solutions of PDE, Vortex flows for incompressible inviscid fluids, weighted Sobolev spaces, Stokes and related (Oseen, etc.) flows, stream function, Babuska-Brezzi ``inf-sup'' condition, Navier-Stokes equations, vector potential, exterior Stokes problem
weak variational formulation, Variational methods for second-order elliptic equations, Variational methods applied to problems in fluid mechanics, Existence of generalized solutions of PDE, Vortex flows for incompressible inviscid fluids, weighted Sobolev spaces, Stokes and related (Oseen, etc.) flows, stream function, Babuska-Brezzi ``inf-sup'' condition, Navier-Stokes equations, vector potential, exterior Stokes problem
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!