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Study of generalized Stokes operator in a thin domain with friction law (case p < 2)
Author(s) -
Dilmi Mohamed,
Dilmi Mourad,
Benseridi Hamid
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4876
Subject(s) - mathematics , uniqueness , domain (mathematical analysis) , work (physics) , operator (biology) , compressibility , mathematical analysis , reynolds number , statement (logic) , variational inequality , law , turbulence , mechanics , physics , biochemistry , chemistry , repressor , gene , transcription factor , political science , thermodynamics
In this work, we consider a mathematical model of an incompressible fluid governed by the generalized Stokes system in a stationary regime in a 3‐dimensional thin domain Ω ϵ with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the estimates on velocity and pressure are proved in a fixed domain. Finally, our main goal concerns the specific Reynolds equation and the uniqueness of the solutionû ϵ ,π ^ ϵare obtained.